Paul Skrzypczyk | Publications

2024

Phys. Rev. Lett

The Dynamical Resource Theory of Informational Non-Equilibrium Preservability

B. Stratton, C.-Y. Hsieh, P. Skrzypczyk

Phys. Rev. Lett 132, 110202 (2024)

Abstract Full Text

Information is instrumental in our understanding of thermodynamics. Their interplay has been studied through completely degenerate Hamiltonians whereby the informational contributions to thermodynamic transformations can be isolated. In this setting, all states other then the maximally mixed state are considered to be in informational non-equilibrium. An important yet still open question is: how to characterise the ability of quantum dynamics to maintain informational non-equilibrium? Here, the dynamical resource theory of informational non-equilibrium preservability is introduced to begin providing an answer to this question. A characterisation of the allowed operations is given for qubit channels and the n dimensional Weyl-covariant channels - a physically relevant subset of the general channels. An operational interpretation of a state discrimination game with Bell state measurements is given. Finally, an explicit link between a channels classical capacity and its ability to maintain informational non-equilibrium is made.

2023

arXiv:2312.03515

The Hadamard gate cannot be replaced by a resource state in universal quantum computation

B. D. M. Jones, N. Linden, P. Skrzypczyk

arXiv:2312.03515 , (2023)

Abstract Full Text

We consider models of quantum computation that involve operations performed on some fixed resourceful quantum state. Examples that fit this paradigm include magic state injection and measurement-based approaches. We introduce a framework that incorporates both of these cases and focus on the role of coherence (or superposition) in this context, as exemplified through the Hadamard gate. We prove that given access to incoherent unitaries (those that are unable to generate superposition from computational basis states, e.g. CNOT, diagonal gates), classical control, computational basis measurements, and any resourceful ancillary state (of arbitrary dimension), it is not possible to implement any coherent unitary (e.g. Hadamard) exactly with non-zero probability. We also consider the approximate case by providing lower bounds for the induced trace distance between the above operations and n Hadamard gates. To demonstrate the stability of this result, this is then extended to a similar no-go result for the case of using k Hadamard gates to exactly implement n>k Hadamard gates.
Phys. Rev. Lett

Maxwell’s Demon walks into Wall Street: Stochastic Thermodynamics meets Expected Utility Theory

A. F. Ducuara, P. Skrzypczyk, F. Buscemi, P. Sidajaya, F. Scarani

Phys. Rev. Lett 131, 197103 (2023)

Abstract Full Text

abstract=The interplay between thermodynamics and information theory has a long history, but its quantitative manifestations are still being explored. We import tools from expected utility theory from economics into stochastic thermodynamics. We prove that, in a process obeying Crooks’ fluctuation relations, every alpha Rényi divergence between the forward process and its reverse has the operational meaning of the “certainty equivalent” of dissipated work (or, more generally, of entropy production) for a player with risk aversion r=alpha−1. The two known cases alpha=1 and alpha=infinity are recovered and receive the new interpretation of being associated to a risk-neutral and an extreme risk-averse player respectively. Among the new results, the condition for alpha=0 describes the behavior of a risk-seeking player willing to bet on the transient violations of the second law. Our approach further leads to a generalized Jarzynski equality, and generalizes to a broader class of statistical divergences.,
arXiv:2309.11968

Quantum complementarity: A novel resource for unambiguous exclusion and encryption

C.-Y. Hsieh, R. Uola, P. Skrzypczyk

arXiv:2309.11968 , (2023)

Abstract Full Text

Complementarity is a phenomenon explaining several core features of quantum theory, such as the well-known uncertainty principle. Roughly speaking, two objects are said to be complementary if being certain about one of them necessarily forbids useful knowledge about the other. Two quantum measurements that do not commute form an example of complementary measurements, and this phenomenon can also be defined for ensembles of states. Although a key quantum feature, it is unclear whether complementarity can be understood more operationally, as a necessary resource in some quantum information task. Here we show this is the case, and relates to a novel task which we term η-unambiguous exclusion. As well as giving complementarity a clear operational definition, this also uncovers the foundational underpinning of unambiguous exclusion tasks for the first time. We further show that a special type of measurement complementarity is equivalent to advantages in certain encryption tasks. Finally, our analysis suggest that complementarity of measurement and state ensemble can be interpreted as strong forms of measurement incompatibility and quantum steering, respectively.
arXiv:2306.07975

Fundamental connections between utility theories of wealth and information theory

A. F. Ducuara, P. Skrzypczyk

arXiv:2306.07975 , (2023)

Abstract Full Text

We establish fundamental connections between utility theories of wealth from the economic sciences and information-theoretic quantities. In particular, we introduce operational tasks based on betting where both gambler and bookmaker have access to side information, or betting tasks with double side information for short. In order to characterise these operational tasks we introduce new conditional Rényi divergences, and explore some of their properties. Furthermore, we introduce an utility theory of wealth ratios, and operationally interpret there the two-parameter (q,r) generalised mutual information measure recently introduced by V. M. Ilić and I. V. Djordjević; it quantifies the advantage provided by side information in betting tasks for utility theories of wealth ratios. Moreover, we show that the Ilić-Djordjević conditional entropy satisfies a type of generalised chain rule, which generalises that of Arimoto-Rényi. Finally, we address the implications of these results on the quantum resource theories of informative measurements and non-constant channels. Altogether, these results further help strengthening the bridge between the theory of expected utility from the economic sciences and Shannon’s theory of information.
Textbook

Semidefinite Programming in Quantum Information Science

P. Skrzypczyk, D. Cavalcanti

Abstract Full Text

Semidefinite programs (SDPs) are a class of optimisation problems that find application in numerous areas of physics, engineering and mathematics. Semidefinite programming is particularly suited to problems in quantum physics and quantum information science. Following a review of the theory of semidefinite programming, the book proceeds to describe how it can be used to address a wide range of important problems from across quantum information science. Specific applications include quantum state, measurement, and channel estimation and discrimination, entanglement detection and quantification, quantum distance measures, and measurement incompatibility. Though SDPs have become an increasingly important tool in quantum information science it’s not yet the kind of mathematics students learn routinely. Assuming only a basic knowledge of linear algebra and quantum physics and quantum information, this graduate-level book provides a unified and accessible presentation of one of the key numerical methods used in quantum information science. Whilst the focus is on the theoretical machinery of SDPs, the authors have provided an accompanying GitHub repository containing example code, covering some of the SDPs studied in this book. Part of IOP Series in Quantum Technology.Key features• Accessible for graduate students in science and mathematics.• A unified and accessible presentation of one of the key numerical methods used in quantum information science.• Written by leading researchers on the topic.• Accompanying GitHub repository with sample code.

2022

arXiv:2203.02593

All quantum measurements are asymptotically equivalent

N. Linden, P. Skrzypczyk

arXiv:2203.02593 , (2022)

Abstract Full Text

We consider the problem of reproducing one quantum measurement given the ability to perform another. In particular, given the availability of a – possibly imperfect – quantum measurement which can be performed multiple times, we study to what extent it can reproduce the measurement statistics and post-measurement state of a second target measurement, in the most general setting where both the available and target measurements are arbitrary generalised quantum measurements. We show that this general problem in fact reduces to the ability to reproduce the statistics of von Neumann measurements, and that in the asymptotic limit of infinitely many uses of the available measurement, a simple protocol based upon ‘classical cloning’ is able to perfectly achieve this task. This shows that asymptotically all (non-trivial) quantum measurements are equivalent. We also study optimal protocols for a fixed number of uses of the available measurement, and show that better protocols than classical cloning can be found in general. Our protocols show that the average error in reproducing a target measurement drops off exponentially fast, and that one can, for example, rapidly improve imperfect measurements by performing them a small number of times. This includes, but is not limited to, improving both noisy and lossy quantum measurements. Finally, we show that in a setting where we perform multiple measurements in parallel, we can moreover achieve finite-rate measurement reproduction, by using block-coding techniques from classical information theory.
PRX Quantum

Characterisation of quantum betting tasks in terms of Arimoto mutual information

A. F. Ducuara, P. Skrzypczyk

PRX Quantum 3, 020366 (2022)

Abstract Full Text

We introduce operational quantum tasks based on betting with risk-aversion - or quantum betting tasks for short - inspired by standard quantum state discrimination and classical horse betting with risk-aversion and side information. In particular, we introduce the operational tasks of quantum state betting (QSB), noisy quantum state betting (nQSB), and quantum channel betting (QCB) played by gamblers with different risk tendencies. We prove that the advantage that informative measurements (non-constant channels) provide in QSB (nQSB) is exactly characterised by Arimoto’s α-mutual information, with the order α determining the risk aversion of the gambler. More generally, we show that Arimoto-type information-theoretic quantities characterise the advantage that resourceful objects offer at playing quantum betting tasks when compared to resourceless objects, for general quantum resource theories (QRTs) of measurements, channels, states, and state-measurement pairs, with arbitrary resources. In limiting cases, we show that QSB (QCB) recovers the known tasks of quantum state (channel) discrimination when α → ∞, and quantum state (channel) exclusion when α → -∞. Inspired by these connections, we also introduce new quantum Rényi divergences for measurements, and derive a new family of resource monotones for the QRT of measurement informativeness. This family of resource monotones recovers in the same limiting cases as above, the generalised robustness and the weight of informativeness. Altogether, these results establish a broad and continuous family of four-way correspondences between operational tasks, mutual information measures, quantum Rényi divergences, and resource monotones, that can be seen to generalise two limiting correspondences that were recently discovered for the QRT of measurement informativeness.

2021

Phys. Rev. Lett

Network Quantum Steering

B. D. M. Jones, I. Šupić, R. Uola, N. Brunner, P. Skrzypczyk

Phys. Rev. Lett 127, 120405 (2021)

Abstract Full Text

The development of large-scale quantum networks promises to bring a multitude of technological applications as well as shed light on foundational topics, such as quantum nonlocality. It is particularly interesting to consider scenarios where sources within the network are statistically independent, which leads to so-called network nonlocality, even when parties perform fixed measurements. Here we promote certain parties to be trusted and introduce the notion of network steering and network local hidden state (NLHS) models within this paradigm of independent sources. In one direction, we show how the results from Bell nonlocality and quantum steering can be used to demonstrate network steering. We further show that it is a genuinely novel effect by exhibiting unsteerable states that nevertheless demonstrate network steering based upon entanglement swapping yielding a form of activation. On the other hand, we provide no-go results for network steering in a large class of scenarios by explicitly constructing NLHS models.
Phys. Rev. Lett

Catalytic Quantum Teleportation

P. Lipka-Bartosik, P. Skrzypczyk

Phys. Rev. Lett 127, 080502 (2021)

Abstract Full Text

Quantum catalysis is an intricate feature of quantum entanglement. It demonstrates that in certain situations the very presence of entanglement can improve one’s abilities of manipulating other entangled states. At the same time, however, it is not clear if using entanglement catalytically can provide additional power for any of the existing quantum protocols. Here we show, for the first time, that catalysis of entanglement can provide a genuine advantage in the task of quantum teleportation. More specifically, we show that extending the standard teleportation protocol by giving Alice and Bob the ability to use entanglement catalytically, allows them to achieve fidelity of teleportation at least as large as the regularisation of the standard teleportation quantifier, the so-called average fidelity of teleportation. Consequently, we show that this regularised quantifier surpasses the standard benchmark for a variety of quantum states, therefore demonstrating that there are quantum states whose ability to teleport can be further improved when assisted with entanglement in a catalytic way. This hints that entanglement catalysis can be a promising new avenue for exploring novel advantages in the quantum domain.
PRX Quantum

Operational Significance of the Quantum Resource Theory of Buscemi Nonlocality

P. Lipka-Bartosik, A. F. Ducuara, T. Purves, P. Skrzypczyk

PRX Quantum 2, 020301 (2021)

Abstract Full Text

Although entanglement is necessary for observing nonlocality in a Bell experiment, there are entangled states that can never be used to demonstrate nonlocal correlations. In a seminal paper Buscemi [Phys. Rev. Lett. \textbf108, 200401 (2012)] extended the standard Bell experiment by allowing Alice and Bob to be asked quantum, instead of classical, questions. This gives rise to a broader notion of nonlocality, one which can be observed for every entangled state. In this work we study a resource theory of this type of nonlocality referred to as Buscemi nonlocality. We propose a geometric quantifier measuring the ability of a given state and local measurements to produce Buscemi nonlocal correlations and prove the following results. First, we show that any distributed measurement that can demonstrate Buscemi nonlocal correlations provides strictly better performance than any distributed measurement that does not use entanglement in the task of distributed state discrimination, and that this advantage is quantified by the geometric quantifier we propose, thus establishing its operational significance. Second, we prove a quantitative relationship between Buscemi nonlocality, the ability to perform nonclassical teleportation, and entanglement. In particular, we show that the maximal amount of Buscemi nonlocality that can be generated using a given state is precisely equal to its entanglement content. Using this relationship, we propose new discrimination tasks for which nonclassical teleportation and entanglement lead to an advantage over their classical counterparts. Third, we interpret Buscemi nonlocality from the perspective of information theory and show that it is related to a single-shot capacity of a quantum-to-classical bipartite channel.
Phys. Rev. X

All States are Universal Catalysts in Quantum Thermodynamics

P. Lipka-Bartosik, P. Skrzypczyk

Phys. Rev. X 11, 011061 (2021)

Abstract Full Text

Quantum catalysis is a fascinating concept that demonstrates how certain transformations can only become possible when given access to a specific resource that has to be returned unaffected. It was first discovered in the context of entanglement theory, and since then, it has been applied in a number of resource-theoretic frameworks, including quantum thermodynamics. Although, in that case, the necessary (and sometimes also sufficient) conditions on the existence of a catalyst are known, almost nothing is known about the precise form of the catalyst state required by the transformation. In particular, it is not clear whether it has to have some special properties or be finely tuned to the desired transformation. In this work, we describe a surprising property of multicopy states: We show that in resource theories governed by majorization, all resourceful states are catalysts for all allowed transformations. In quantum thermodynamics, this means that the so-called “second laws of thermodynamics” do not require a fine-tuned catalyst; rather, any state, given sufficiently many copies, can serve as a useful catalyst. These analytic results are accompanied by several numerical investigations that indicate that neither a multicopy form nor a very-large-dimension catalyst is required to activate most allowed transformations catalytically.

2020

Phys. Rev. Research

Multiobject operational tasks for convex quantum resource theories of state-measurement pairs

A. F. Ducuara, P. Lipka-Bartosik, P. Skrzypczyk

Phys. Rev. Research 2, 033374 (2020)

Abstract Full Text

The prevalent modus operandi within the framework of quantum resource theories has been to characterize and harness the resources within single objects, in what we can call single-object quantum resource theories. One can wonder, however, whether the resources contained within multiple different types of objects, now in a multiobject quantum resource theory, can simultaneously be exploited for the benefit of an operational task. In this work, we introduce examples of such multiobject operational tasks in the form of subchannel discrimination and subchannel exclusion games, in which the player harnesses the resources contained within the composite object of a state-measurement pair. We prove that for any state-measurement pair in which either of them is resourceful, there exist discrimination and exclusion games for which such a pair outperforms any possible free state-measurement pair. These results hold for arbitrary convex resources of states, and arbitrary convex resources of measurements where the set of free measurements is closed under classical post-processing. Furthermore, we prove that the advantage in these multiobject operational tasks is determined, in a multiplicative manner, by the resource quantifiers of: generalized robustness of resource of both state and measurement for discrimination games and weight of resource of both state and measurement for exclusion games.
Phys. Rev. Lett.

Operational Interpretation of Weight-Based Resource Quantifiers in Convex Quantum Resource Theories

A. F. Ducuara, P. Skrzypczyk

Phys. Rev. Lett. 125, 110401 (2020)

Abstract Full Text

We introduce the resource quantifier of weight of resource for convex quantum resource theories of states and measurements with arbitrary resources. We show that it captures the advantage that a resourceful state (measurement) offers over all possible free states (measurements) in the operational task of exclusion of subchannels (states). Furthermore, we introduce information-theoretic quantities related to exclusion for quantum channels and find a connection between the weight of resource of a measurement and the exclusion-type information of quantum-to-classical channels. Our results apply to the resource theory of entanglement in which the weight of resource is known as the best-separable approximation or Lewenstein-Sanpera decomposition introduced in 1998. Consequently, the results found here provide an operational interpretation to this 21-year-old entanglement quantifier.
Phys. Rev. Lett.

Bipartite Postquantum Steering in Generalized Scenarios

A. B. Sainz, M. J. Hoban, P. Skrzypczyk, L. Aolita

Phys. Rev. Lett. 125, 050404 (2020)

Abstract Full Text

The study of stronger-than-quantum effects is a fruitful line of research that provides valuable insight into quantum theory. Unfortunately, traditional bipartite steering scenarios can always be explained by quantum theory. Here, we show that, by relaxing this traditional setup, bipartite steering incompatible with quantum theory is possible. The two scenarios we describe, which still feature Alice remotely steering Bob’s system, are (i) one where Bob also has an input and operates on his subsystem, and (ii) the “instrumental steering” scenario. We show that such bipartite postquantum steering is a genuinely new type of postquantum nonlocality, which does not follow from postquantum Bell nonlocality. In addition, we present a method to bound quantum violations of steering inequalities in these scenarios.
Quantum

Device-independent quantum key distribution with single-photon sources

J. Kołodyński, A. Máttar, P. Skrzypczyk, E. Woodhead, D. Cavalcanti, K. Banaszek, A. Acín

Quantum 4, 260 (2020)

Abstract Full Text

Device-independent quantum key distribution protocols allow two honest users to establish a secret key with minimal levels of trust on the provider, as security is proven without any assumption on the inner working of the devices used for the distribution. Unfortunately, the implementation of these protocols is challenging, as it requires the observation of a large Bell-inequality violation between the two distant users. Here, we introduce novel photonic protocols for device-independent quantum key distribution exploiting single-photon sources and heralding-type architectures. The heralding process is designed so that transmission losses become irrelevant for security. We then show how the use of single-photon sources for entanglement distribution in these architectures, instead of standard entangled-pair generation schemes, provides significant improvements on the attainable key rates and distances over previous proposals. Given the current progress in single-photon sources, our work opens up a promising avenue for device-independent quantum key distribution implementations.
Optica

Multi-core fiber integrated multi-port beam splitters for quantum information processing

J. Cariñe, G. Cañas, P. Skrzypczyk, I. Šupić, N. Guerrero, T. Garcia, L. Pereira, M. a. S. Prosser, G. B. Xavier, A. Delgado, S. P. Walborn, D. Cavalcanti, G. Lima

Optica 7, 542–550 (2020)

Abstract Full Text

Multi-port beam splitters are cornerstone devices for high-dimensional quantum information tasks, which can outperform the two-dimensional ones. Nonetheless, the fabrication of such devices has proven to be challenging with progress only recently achieved with the advent of integrated photonics. Here, we report on the production of high-quality N×N (with N=4,7) multi-port beam splitters based on a new scheme for manipulating multi-core optical fibers. By exploring their compatibility with optical fiber components, we create four-dimensional quantum systems and implement the measurement-device-independent random number generation task with a programmable four-arm interferometer operating at a 2 MHz repetition rate. Due to the high visibilities observed, we surpass the one-bit limit of binary protocols and attain 1.23 bits of certified private randomness per experimental round. Our result demonstrates that fast switching, low loss, and high optical quality for high-dimensional quantum information can be simultaneously achieved with multi-core fiber technology.
Phys. Rev. Research

Complexity of compatible measurements

P. Skrzypczyk, M. J. Hoban, A. B. Sainz, N. Linden

Phys. Rev. Research 2, 023292 (2020)

Abstract Full Text

Measurement incompatibility is one of the basic aspects of quantum theory. Here we study the structure of the set of compatible, i.e., jointly measurable, measurements. We are interested in whether or not there exist compatible measurements whose parent is maximally complex, in the sense of requiring a number of outcomes exponential in the number of measurements, and related questions. Although we show this to be the case in a number of simple scenarios, we show that generically it cannot happen, by proving an upper bound on the number of outcomes of a parent measurement that is linear in the number of compatible measurements. We discuss why this does not trivialize the problem of finding parent measurements, but rather shows that a trade-off between memory and time can be achieved. Finally, we also investigate the complexity of extremal compatible measurements in regimes where our bound is not tight and uncover rich structure.
Phys. Rev. Res.

Operational advantages provided by nonclassical teleportation

P. Lipka-Bartosik, P. Skrzypczyk

Phys. Rev. Res. 2, 023029 (2020)

Abstract Full Text

The standard benchmark for teleportation is the average fidelity of teleportation and according to this benchmark not all states are useful for teleportation. It was recently shown, however, that all entangled states lead to nonclassical teleportation, with there being no classical scheme able to reproduce the states teleported to Bob. Here we study the operational significance of this result. On the one hand, we demonstrate that every state is useful for teleportation if a generalization of the average fidelity of teleportation is considered which concerns teleporting quantum correlations. On the other hand, we show the strength of a particular entangled state and entangled measurement for teleportation—as quantified by the robustness of teleportation—precisely characterizes their ability to offer an advantage in the task of subchannel discrimination with side information. This connection allows us to prove that every entangled state outperforms all separable states when acting as a quantum memory in this discrimination task. Finally, within the context of a resource theory of teleportation, we show that the two operational tasks considered provide complete sets of monotones for two partial orders based on the notion of teleportation simulation, one classical and one quantum.

2019

Quantum

Exploring the limits of no backwards in time signalling

Y. Guryanova, R. Silva, A. J. Short, P. Skrzypczyk, N. Brunner, S. Popescu

Quantum 3, 211 (2019)

Abstract Full Text

We present an operational and model-independent framework to investigate the concept of no-backwards-in-time signalling. We define no-backwards-in-time signalling conditions, closely related to the spatial no-signalling conditions. These allow for theoretical possibilities in which the future affects the past, nevertheless without signalling backwards in time. This is analogous to non-local but no-signalling spatial correlations. Furthermore, our results shed new light on situations with indefinite causal structure and their connection to quantum theory.
Phys. Rev. Lett.

All Sets of Incompatible Measurements give an Advantage in Quantum State Discrimination

P. Skrzypczyk, I. Šupić, D. Cavalcanti

Phys. Rev. Lett. 122, 130403 (2019)

Abstract Full Text

Some quantum measurements cannot be performed simultaneously; i.e., they are incompatible. Here we show that every set of incompatible measurements provides an advantage over compatible ones in a suitably chosen quantum state discrimination task. This is proven by showing that the robustness of incompatibility, a quantifier of how much noise a set of measurements tolerates before becoming compatible, has an operational interpretation as the advantage in an optimally chosen discrimination task. We also show that if we take a resource-theory perspective of measurement incompatibility, then the guessing probability in discrimination tasks of this type forms a complete set of monotones that completely characterize the partial order in the resource theory. Finally, we make use of previously known relations between measurement incompatibility and Einstein-Podolsky-Rosen steering to also relate the latter with quantum state discrimination.
Phys. Rev. A

Methods to estimate entanglement in teleportation experiments

I. Šupić, P. Skrzypczyk, D. Cavalcanti

Phys. Rev. A 99, 032334 (2019)

Abstract Full Text

Quantum state teleportation is a protocol where a shared entangled state is used as a quantum channel to transmit quantum information between distinct locations. Here we consider the task of estimating entanglement of the underlying shared state in teleportation protocols. We show that the data accessible in a teleportation experiment allows us to put a lower bound on some entanglement measures, such as entanglement negativity and robustness. Furthermore, we show cases in which the lower bounds are tight. The introduced lower bounds can also be interpreted as quantifiers of the nonclassicality of a teleportation experiment. Thus, our findings provide a quantitative relation between teleportation and entanglement.
Phys. Rev. Lett. Editor’s Suggestion

Robustness of Measurement, Discrimination Games, and Accessible Information

P. Skrzypczyk, N. Linden

Phys. Rev. Lett. 122, 140403 (2019)

Abstract Full Text arXiv

We introduce a resource theory of measurement informativeness. This allows us to define an associated quantifier, which we call the robustness of measurement. It describes how much “noise” must be added to a measurement before it becomes completely uninformative. We show that this geometric quantifier has operational significance in terms of the advantage the measurement provides over guessing at random in a suitably chosen state discrimination game and that it is the single-shot generalization of the accessible information of a certain quantum-to-classical channel. Using this insight, we further show that the recently introduced robustness of asymmetry or coherence is the single-shot generalization of the accessible information of an ensemble. Finally, we discuss more generally the connection between robustness-based measures, discrimination problems, and information-theoretic quantities.
Phys. Rev. Lett.

Quantifying Measurement Incompatibility of Mutually Unbiased Bases

S. Designolle, P. Skrzypczyk, F. Fröwis, N. Brunner

Phys. Rev. Lett. 122, 050402 (2019)

Abstract Full Text

Quantum measurements based on mutually unbiased bases are commonly used in quantum information processing, as they are generally viewed as being maximally incompatible and complementary. Here we quantify precisely the degree of incompatibility of mutually unbiased bases (MUB) using the notion of noise robustness. Specifically, for sets of k MUB in dimension d, we provide upper and lower bounds on this quantity. Notably, we get a tight bound in several cases, in particular for complete sets of k = d + 1 MUB (using the standard construction for d being a prime power). On the way, we also derive a general upper bound on the noise robustness for an arbitrary set of quantum measurements. Moreover, we prove the existence of sets of k MUB that are operationally inequivalent, as they feature different noise robustness, and we provide a lower bound on the number of such inequivalent sets up to dimension 32. Finally, we discuss applications of our results for Einstein-Podolsky-Rosen steering.

2018

Phys. Rev. Lett.

Experimental Study of Nonclassical Teleportation Beyond Average Fidelity

G. Carvacho, F. Andreoli, L. Santodonato, M. Bentivegna, V. D’Ambrosio, P. Skrzypczyk, I. Šupić, D. Cavalcanti, F. Sciarrino

Phys. Rev. Lett. 121, 140501 (2018)

Abstract Full Text

Quantum teleportation establishes a correspondence between an entangled state shared by two separate parties that can communicate classically and the presence of a quantum channel connecting the two parties. The standard benchmark for quantum teleportation, based on the average fidelity between the input and output states, indicates that some entangled states do not lead to channels which can be certified to be quantum. It was recently shown that if one considers a finer-grained witness, then all entangled states can be certified to produce a nonclassical teleportation channel. Here we experimentally demonstrate a complete characterization of a new family of such witnesses, of the type proposed in Phys. Rev. Lett. 119, 110501 (2017) under different conditions of noise. We report nonclassical teleportation using quantum states that cannot achieve average fidelity of teleportation above the classical limit. We further use the violation of these witnesses to estimate the negativity of the shared state. Our results have fundamental implications in quantum information protocols and may also lead to new applications and quality certification of quantum technologies.
New J. Phys.

A formalism for steering with local quantum measurements

A. B. Sainz, L. Aolita, M. Piani, M. J. Hoban, P. Skrzypczyk

New J. Phys. 20, 083040 (2018)

Abstract Full Text

We develop a unified approach to classical, quantum and post-quantum steering. The framework is based on uncharacterised (black-box) parties performing quantum measurements on their share of a (possibly unphysical) quantum state, and its starting point is the characterisation of general no-signalling assemblages via non-positive local hidden-state models, which will be defined in this work. By developing a connection to entanglement witnesses, this formalism allows for new definitions of families of assemblages, in particular via (i) non-decomposable positive maps and (ii) unextendible product bases. The former proves to be useful for constructing post-quantum assemblages with the built-in feature of yielding only quantum correlations in Bell experiments, while the latter always gives certifiably post-quantum assemblages. Finally, our framework is equipped with an inherent quantifier of post-quantum steering, which we call the negativity of post-quantum steering. We postulate that post-quantum steering should not increase under one-way quantum operations from the steered parties to the steering parties, and we show that, in this sense, the negativity of post-quantum steering is a convex post-quantum-steering monotone.
Phys. Rev. Lett.

Maximal Randomness Generation from Steering Inequality Violations Using Qudits

P. Skrzypczyk, D. Cavalcanti

Phys. Rev. Lett. 120, 260401 (2018)

Abstract Full Text

We consider the generation of randomness based upon the observed violation of an Einstein-Podolsky-Rosen (EPR) steering inequality, known as one-sided device-independent randomness generation. We show that in the simplest scenario—involving only two parties and two measurements for the uncharacterised party with d outcomes—that there exist EPR steering inequalities whose maximal violation certifies maximal randomness generation, equal to log(d) bits. We further show that all pure partially entangled full-Schmidt-rank states in all dimensions can achieve maximal violation of these inequalities, and thus lead to maximal randomness generation in the one-sided device-independent setting. More generally, the amount of randomness that can be generated is given by a semidefinite program, which we use to study the behavior for nonmaximal violations of the inequalities.
Science

Multidimensional quantum entanglement with large-scale integrated optics

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mančinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acín, K. Rottwitt, L. K. Oxenløwe, J. L. O’Brien, A. Laing, M. G. Thompson

Science 360, 285 (2018)

Abstract Full Text

The ability to control multidimensional quantum systems is central to the development of advanced quantum technologies. We demonstrate a multidimensional integrated quantum photonic platform able to generate, control, and analyze high-dimensional entanglement. A programmable bipartite entangled system is realized with dimensions up to 15 x 15 on a large-scale silicon photonics quantum circuit. The device integrates more than 550 photonic components on a single chip, including 16 identical photon-pair sources. We verify the high precision, generality, and controllability of our multidimensional technology, and further exploit these abilities to demonstrate previously unexplored quantum applications, such as quantum randomness expansion and self-testing on multidimensional states. Our work provides an experimental platform for the development of multidimensional quantum technologies.

2017

New J. Phys.

Connecting processes with indefinite causal order and multi-time quantum states

R. Silva, Y Guryanova, A. J. Short, P. Skrzypczyk, N. Brunner, S. Popescu

New J. Phys. 19, 103022 (2017)

Abstract Full Text

Recently, the possible existence of quantum processes with indefinite causal order has been extensively discussed, in particular using the formalism of process matrices. Here we give a new perspective on this question, by establishing a direct connection to the theory of multi-time quantum states. Specifically, we show that process matrices are equivalent to a particular class of pre- and post-selected quantum states. This offers a new conceptual point of view to the nature of process matrices. Our results also provide an explicit recipe to experimentally implement any process matrix in a probabilistic way, and allow us to generalize some of the previously known properties of process matrices. Finally we raise the issue of the difference between the notions of indefinite temporal order and indefinite causal order, and show that one can have indefinite causal order even with definite temporal order.
Phys. Rev. Lett. Editor’s Suggestion

All Entangled States can Demonstrate Nonclassical Teleportation

D. Cavalcanti, P. Skrzypczyk, I. Šupić

Phys. Rev. Lett. 119, 110501 (2017)

Abstract Full Text

Quantum teleportation, the process by which Alice can transfer an unknown quantum state to Bob by using preshared entanglement and classical communication, is one of the cornerstones of quantum information. The standard benchmark for certifying quantum teleportation consists in surpassing the maximum average fidelity between the teleported and the target states that can be achieved classically. According to this figure of merit, not all entangled states are useful for teleportation. Here we propose a new benchmark that uses the full information available in a teleportation experiment and prove that all entangled states can implement a quantum channel which cannot be reproduced classically. We introduce the idea of nonclassical teleportation witness to certify if a teleportation experiment is genuinely quantum and discuss how to quantify this phenomenon. Our work provides new techniques for studying teleportation that can be immediately applied to certify the quality of quantum technologies.
Phys. Rev. A

Measurement-device-independent entanglement and randomness estimation in quantum networks

I. Šupić, P. Skrzypczyk, D. Cavalcanti

Phys. Rev. A 95, 042340 (2017)

Abstract Full Text

Detection of entanglement in quantum networks consisting of many parties is one of the important steps toward building quantum communication and computation networks. We consider a scenario where the measurement devices used for this certification are uncharacterized. In this case, it is well known that by using quantum states as inputs for the measurement devices it is possible to detect any entangled state (a situation known as measurement-device-independent entanglement witnessing). Here we go beyond entanglement detection and provide methods to estimate the amount of entanglement in a quantum network. We also consider the task of randomness certification and show that randomness can be certified in a variety of cases, including single-partite experiments or setups using only separable states.
Quantum Sci. Tech.

Experimental multipartite entanglement and randomness certification of the W state in the quantum steering scenario

A. Máttar, P. Skrzypczyk, G. H. Aguilar, R. V. Nery, P. H. Souto Ribeiro, S. P. Walborn, D. Cavalcanti

Quantum Sci. Tech. 2, 015011 (2017)

Abstract Full Text

Recently, Cavalcanti et al (2015) proposed a method to certify the presence of entanglement in asymmetric networks, where some users do not have control over the measurements they are performing. Such asymmetry naturally emerges in realistic situations, such as in cryptographic protocols over quantum networks. Here we implement such ‘semi-device-independent’ techniques to experimentally witness all types of entanglement on a three-qubit photonic W state. Furthermore, we analyse the amount of genuine randomness that can be certified in this scenario from any bipartition of the three-qubit W state.
Rep. Prog. Phys. Review

Quantum steering: a review with focus on semidefinite programming

D. Cavalcanti, P. Skrzypczyk

Rep. Prog. Phys. 80, 024001 (2017)

Abstract Full Text

Quantum steering refers to the non-classical correlations that can be observed between the outcomes of measurements applied on half of an entangled state and the resulting post-measured states that are left with the other party. From an operational point of view, a steering test can be seen as an entanglement test where one of the parties performs uncharacterised measurements. Thus, quantum steering is a form of quantum inseparability that lies in between the well-known notions of Bell nonlocality and entanglement. Moreover, quantum steering is also related to several asymmetric quantum information protocols where some of the parties are considered untrusted. Because of these facts, quantum steering has received a lot of attention both theoretically and experimentally. The main goal of this review is to give an overview of how to characterise quantum steering through semidefinite programming. This characterisation provides efficient numerical methods to address a number of problems, including steering detection, quantification, and applications. We also give a brief overview of some important results that are not directly related to semidefinite programming. Finally, we make available a collection of semidefinite programming codes that can be used to study the topics discussed in this article.

2016

Phys. Rev. Lett.

General Method for Constructing Local Hidden Variable Models for Entangled Quantum States

D. Cavalcanti, L. Guerini, R. Rabelo, P. Skrzypczyk

Phys. Rev. Lett. 117, 190401 (2016)

Abstract Full Text

Entanglement allows for the nonlocality of quantum theory, which is the resource behind device-independent quantum information protocols. However, not all entangled quantum states display nonlocality. A central question is to determine the precise relation between entanglement and nonlocality. Here we present the first general test to decide whether a quantum state is local, and show that the test can be implemented by semidefinite programing. This method can be applied to any given state and for the construction of new examples of states with local hidden variable models for both projective and general measurements. As applications, we provide a lower-bound estimate of the fraction of two-qubit local entangled states and present new explicit examples of such states, including those that arise from physical noise models, Bell-diagonal states, and noisy Greenberger-Horne-Zeilinger and W states.
Phys. Rev. A

Adjusting inequalities for detection-loophole-free steering experiments

A. B. Sainz, Y. Guryanova, W. McCutcheon, P. Skrzypczyk

Phys. Rev. A 94, 032122 (2016)

Abstract Full Text

We study the problem of certifying quantum steering in a detection-loophole-free manner in experimental situations that require postselection. We present a method to find the modified local-hidden-state bound of steering inequalities in such a postselected scenario. We then present a construction of linear steering inequalities in arbitrary finite dimension and show that they certify steering in a loophole-free manner as long as the detection efficiencies are above the known bound below which steering can never be demonstrated. We also show how our method extends to the scenarios of multipartite steering and Bell nonlocality, in the general case where there can be correlations between the losses of the different parties. In both cases we present examples to demonstrate the techniques developed.
Phys. Rev. E

Performance of autonomous quantum thermal machines: Hilbert space dimension as a thermodynamical resource

R. Silva, G. Manzano, P. Skrzypczyk, N. Brunner

Phys. Rev. E 94, 032120 (2016)

Abstract Full Text

Multilevel autonomous quantum thermal machines are discussed. In particular, we explore the relationship between the size of the machine (captured by Hilbert space dimension) and the performance of the machine. Using the concepts of virtual qubits and virtual temperatures, we show that higher dimensional machines can outperform smaller ones. For instance, by considering refrigerators with more levels, lower temperatures can be achieved, as well as higher power. We discuss the optimal design for refrigerators of a given dimension. As a consequence we obtain a statement of the third law in terms of Hilbert space dimension: Reaching absolute zero temperature requires infinite dimension. These results demonstrate that Hilbert space dimension should be considered a thermodynamic resource.
Phys. Rev. A

Classical communication cost of quantum steering

A. B. Sainz, L. Aolita, N. Brunner, R. Gallego, P. Skrzypczyk

Phys. Rev. A 94, 012308 (2016)

Abstract Full Text

Quantum steering is observed when performing appropriate local measurements on an entangled state. Here we discuss the possibility of simulating classically this effect, using classical communication instead of entanglement. We show that infinite communication is necessary for exactly simulating steering for any pure entangled state, as well as for a class of mixed entangled states. Moreover, we discuss the communication cost of steering for general entangled states, as well as approximate simulation. Our findings reveal striking differences between Bell nonlocality and steering and provide a natural way of measuring the strength of the latter.
Nature Commun.

Thermodynamics of quantum systems with multiple conserved quantities

Y Guryanova, S. Popescu, A. J. Short, R. Silva, P. Skrzypczyk

Nature Commun. 7, 12049 (2016)

Abstract Full Text

Recently, there has been much progress in understanding the thermodynamics of quantum systems, even for small individual systems. Most of this work has focused on the standard case where energy is the only conserved quantity. Here we consider a generalization of this work to deal with multiple conserved quantities. Each conserved quantity, which, importantly, need not commute with the rest, can be extracted and stored in its own battery. Unlike the standard case, in which the amount of extractable energy is constrained, here there is no limit on how much of any individual conserved quantity can be extracted. However, other conserved quantities must be supplied, and the second law constrains the combination of extractable quantities and the trade-offs between them. We present explicit protocols that allow us to perform arbitrarily good trade-offs and extract arbitrarily good combinations of conserved quantities from individual quantum systems.
Phys. Rev. A

Quantitative relations between measurement incompatibility, quantum steering, and nonlocality

D. Cavalcanti, P. Skrzypczyk

Phys. Rev. A 93, 052112 (2016)

Abstract Full Text

The certification of Bell nonlocality or quantum steering implies the use of incompatible measurements. Here we make this connection quantitative. We show how to strengthen robustness-based steering and nonlocality quantifiers in order that they give strong lower bounds to previously proposed incompatibility quantifiers. Our results can be seen from two perspectives. On the one hand, they can be used to estimate how much steering or nonlocality can be demonstrated with a given set of measurements. On the other hand, they give one-sided device-independent and device-independent ways of estimating measurement incompatibility.
Phys. Rev. A

Necessary detection efficiencies for secure quantum key distribution and bound randomness

A. Acín, D. Cavalcanti, E. Passaro, S. Pironio, P. Skrzypczyk

Phys. Rev. A 93, 012319 (2016)

Abstract Full Text

In recent years, several hacking attacks have broken the security of quantum cryptography implementations by exploiting the presence of losses and the ability of the eavesdropper to tune detection efficiencies. We present a simple attack of this form that applies to any protocol in which the key is constructed from the results of untrusted measurements performed on particles coming from an insecure source or channel. Because of its generality, the attack applies to a large class of protocols, from standard prepare-and-measure to device-independent schemes. Our attack gives bounds on the critical detection efficiencies necessary for secure quantum key distribution, which show that the implementation of most partly device-independent solutions is, from the point of view of detection efficiency, almost as demanding as fully device-independent ones. We also show how our attack implies the existence of a form of bound randomness, namely nonlocal correlations in which a nonsignalling eavesdropper can find out a posteriori the result of any implemented measurement.
J. Phys. A: Math. Theor. Review

The role of quantum information in thermodynamics—a topical review

J. Goold, M. Huber, A. Riera, L. Rio, P. Skrzypczyk

J. Phys. A: Math. Theor. 49, 143001 (2016)

Abstract Full Text

This topical review article gives an overview of the interplay between quantum information theory and thermodynamics of quantum systems. We focus on several trending topics including the foundations of statistical mechanics, resource theories, entanglement in thermodynamic settings, fluctuation theorems and thermal machines. This is not a comprehensive review of the diverse field of quantum thermodynamics; rather, it is a convenient entry point for the thermo-curious information theorist. Furthermore this review should facilitate the unification and understanding of different interdisciplinary approaches emerging in research groups around the world.

2015

Phys. Rev. Lett.

Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems

I. Kogias, P. Skrzypczyk, D. Cavalcanti, A. Acín, G. Adesso

Phys. Rev. Lett. 115, 210401 (2015)

Abstract Full Text

Einstein-Podolsky-Rosen steering is a manifestation of quantum correlations exhibited by quantum systems that allows for entanglement certification when one of the subsystems is not characterized. Detecting the steerability of quantum states is essential to assess their suitability for quantum information protocols with partially trusted devices. We provide a hierarchy of sufficient conditions for the steerability of bipartite quantum states of any dimension, including continuous variable states. Previously known steering criteria are recovered as special cases of our approach. The proposed method allows us to derive optimal steering witnesses for arbitrary families of quantum states and provides a systematic framework to analytically derive nonlinear steering criteria. We discuss relevant examples and, in particular, provide an optimal steering witness for a lossy single-photon Bell state; the witness can be implemented just by linear optics and homodyne detection and detects steering with a higher loss tolerance than any other known method. Our approach is readily applicable to multipartite steering detection and to the characterization of joint measurability.
Phys. Rev. Lett.

Postquantum Steering

A. B. Sainz, N. Brunner, D. Cavalcanti, P. Skrzypczyk, T. Vértesi

Phys. Rev. Lett. 115, 190403 (2015)

Abstract Full Text

The discovery of postquantum nonlocality, i.e., the existence of nonlocal correlations that are stronger than any quantum correlations but nevertheless consistent with the no-signaling principle, has deepened our understanding of the foundations of quantum theory. In this work, we investigate whether the phenomenon of Einstein-Podolsky-Rosen steering, a different form of quantum nonlocality, can also be generalized beyond quantum theory. While post-quantum steering does not exist in the bipartite case, we prove its existence in the case of three observers. Importantly, we show that postquantum steering is a genuinely new phenomenon, fundamentally different from postquantum nonlocality. Our results provide new insight into the nonlocal correlations of multipartite quantum systems.
New J. Phys.

Optimal randomness certification in the quantum steering and prepare-and-measure scenarios

E. Passaro, D. Cavalcanti, P. Skrzypczyk, A. Acín

New J. Phys. 17, 113010 (2015)

Abstract Full Text

Quantum mechanics predicts the existence of intrinsically random processes. Contrary to classical randomness, this lack of predictability can not be attributed to ignorance or lack of control. Here we find the optimal method to quantify the amount of local or global randomness that can be extracted in two scenarios: (i) the quantum steering scenario, where two parties measure a bipartite system in an unknown state but one of them does not trust his measurement apparatus, and (ii) the prepare-and-measure scenario, where additionally the quantum state is known. We use our methods to compute the maximal amount of local and global randomness that can be certified by measuring systems subject to noise and losses and show that local randomness can be certified from a single measurement if and only if the detectors used in the test have detection efficiency higher than 50%.
Phys. Rev. X APS Synopsis

Extractable Work from Correlations

M. Perarnau-Llobet, K. V. Hovhannisyan, M. Huber, P. Skrzypczyk, N. Brunner, A. Acín

Phys. Rev. X 5, 041011 (2015)

Abstract Full Text

Work and quantum correlations are two fundamental resources in thermodynamics and quantum information theory. In this work, we study how to use correlations among quantum systems to optimally store work. We analyze this question for isolated quantum ensembles, where the work can be naturally divided into two contributions: a local contribution from each system and a global contribution originating from correlations among systems. We focus on the latter and consider quantum systems that are locally thermal, thus from which any extractable work can only come from correlations. We compute the maximum extractable work for general entangled states, separable states, and states with fixed entropy. Our results show that while entanglement gives an advantage for small quantum ensembles, this gain vanishes for a large number of systems.
Phys. Rev. E

Most energetic passive states

M. Perarnau-Llobet, K. V. Hovhannisyan, M. Huber, P. Skrzypczyk, J. Tura, A. Acín

Phys. Rev. E 92, 042147 (2015)

Abstract Full Text

Passive states are defined as those states that do not allow for work extraction in a cyclic (unitary) process. Within the set of passive states, thermal states are the most stable ones: they maximize the entropy for a given energy, and similarly they minimize the energy for a given entropy. Here we find the passive states lying in the other extreme, i.e., those that maximize the energy for a given entropy, which we show also minimize the entropy when the energy is fixed. These extremal properties make these states useful to obtain fundamental bounds for the thermodynamics of finite-dimensional quantum systems, which we show in several scenarios.
Phys. Rev. A

Loss-tolerant Einstein-Podolsky-Rosen steering for arbitrary-dimensional states: Joint measurability and unbounded violations under losses

P. Skrzypczyk, D. Cavalcanti

Phys. Rev. A 92, 022354 (2015)

Abstract Full Text

We show how to construct loss-tolerant linear steering inequalities using a generic set of von Neumann measurements that are violated by d-dimensional states, and that rely only upon a simple property of the set of measurements used (the maximal overlap between measurement directions). Using these inequalities we show that the critical detection efficiency above which n von Neumann measurements can demonstrate steering is 1/n. We show furthermore that using our construction and high-dimensional states allows for steering demonstrations which are also highly robust to depolarizing noise and produce unbounded violations in the presence of loss. Finally, our results provide an explicit means to certify the nonjoint measurability of any set of inefficient von Neuman measurements.
Nature Commun.

Detection of entanglement in asymmetric quantum networks and multipartite quantum steering

D. Cavalcanti, P. Skrzypczyk, G. H. Aguilar, R. V. Nery, P. H. Souto Ribeiro, S. P. Walborn

Nature Commun. 6, 7941 (2015)

Abstract Full Text

The future of quantum communication relies on quantum networks composed by observers sharing multipartite quantum states. The certification of multipartite entanglement will be crucial to the usefulness of these networks. In many real situations it is natural to assume that some observers are more trusted than others in the sense that they have more knowledge of their measurement apparatuses. Here we propose a general method to certify all kinds of multipartite entanglement in this asymmetric scenario and experimentally demonstrate it in an optical experiment. Our results, which can be seen as a definition of genuine multipartite quantum steering, give a method to detect entanglement in a scenario in between the standard entanglement and fully device-independent scenarios, and provide a basis for semi-device-independent cryptographic applications in quantum networks.
Phys. Rev. E

Small quantum absorption refrigerator with reversed couplings

R. Silva, P. Skrzypczyk, N. Brunner

Phys. Rev. E 92, 012136 (2015)

Abstract Full Text

Small quantum absorption refrigerators have recently attracted renewed attention. Here we present a missing design of a two-qubit fridge, the main feature of which is that one of the two machine qubits is itself maintained at a temperature colder than the cold bath. This is achieved by “reversing” the couplings to the baths compared to previous designs, where only a transition is maintained cold. We characterize the working regime and the efficiency of the fridge. We demonstrate the soundness of the model by deriving and solving a master equation. Finally, we discuss the performance of the fridge, in particular the heat current extracted from the cold bath. We show that our model performs comparably to the standard three-level quantum fridge and thus appears appealing for possible implementations of nanoscale thermal machines.
New J. Phys.

Thermodynamic cost of creating correlations

M. Huber, M. Perarnau-Llobet, K. V. Hovhannisyan, Skrzypczyk P., C. Klöckl, N. Brunner, A. Acín

New J. Phys. 17, 065008 (2015)

Abstract Full Text

We investigate the fundamental limitations imposed by thermodynamics for creating correlations. Considering a collection of initially uncorrelated thermal quantum systems, we ask how much classical and quantum correlations can be obtained via a cyclic Hamiltonian process. We derive bounds on both the mutual information and entanglement of formation, as a function of the temperature of the systems and the available energy. While for a finite number of systems there is a maximal temperature allowing for the creation of entanglement, we show that genuine multipartite entanglement—the strongest form of entanglement in multipartite systems—can be created at any finite temperature when sufficiently many systems are considered. This approach may find applications, e.g. in quantum information processing, for physical platforms in which thermodynamic considerations cannot be ignored.
Phys. Rev. E

Passivity, complete passivity, and virtual temperatures

P. Skrzypczyk, R. Silva, N. Brunner

Phys. Rev. E 91, 052133 (2015)

Abstract Full Text

We give a simple and intuitive proof that the only states which are completely passive, i.e., those states from which work cannot be extracted even with infinitely many copies, are Gibbs states at positive temperatures. The proof makes use of the idea of virtual temperatures, i.e., the association of temperatures to pairs of energy levels (transitions). We show that (1) passive states are those where every transition is at a positive temperature and (2) completely passive states are those where every transition is at the same positive temperature.
New J. Phys.

Optimal randomness generation from optical Bell experiments

A. Máttar, P. Skrzypczyk, J. Bohr Brask, D. Cavalcanti, A. Acín

New J. Phys. 17, 022003 (2015)

Abstract Full Text

Genuine randomness can be certified from Bell tests without any detailed assumptions on the working of the devices with which the test is implemented. An important class of experiments for implementing such tests is optical setups based on polarization measurements of entangled photons distributed from a spontaneous parametric down conversion source. Here we compute the maximal amount of randomness which can be certified in such setups under realistic conditions. We provide relevant yet unexpected numerical values for the physical parameters and achieve four times more randomness than previous methods.

2014

New J. Phys.

Dimension of physical systems, information processing, and thermodynamics

N. Brunner, M. Kaplan, A. Leverrier, P. Skrzypczyk

New J. Phys. 16, 123050 (2014)

Abstract Full Text

We ask how quantum theory compares to more general physical theories from the point of view of dimension. To do so, we first give two model-independent definitions of the dimension of physical systems, based on measurements and the capacity of storing information. While both definitions are equivalent in classical and quantum mechanics, they are different in generalized probabilistic theories. We discuss in detail the case of a theory known as ‘boxworld’, and show that such a theory features systems with dimension mismatch. This dimension mismatch can be made arbitrarily large using an amplification procedure. Furthermore, we show that the dimension mismatch of boxworld has strong consequences on its power for performing information-theoretic tasks, leading to the collapse of communication complexity and to the violation of information causality. Finally, we discuss the consequences of a dimension mismatch from the perspective of thermodynamics, and ask whether this effect could break Landauerʼs erasure principle and thus the second law.
Phys. Rev. A

Nonlocal correlations in the star-network configuration

A. Tavakoli, P. Skrzypczyk, D. Cavalcanti, A. Acín

Phys. Rev. A 90, 062109 (2014)

Abstract Full Text

The concept of bilocality was introduced to study the correlations which arise in an entanglement-swapping scenario, where one has two sources which can naturally be taken to be independent. This additional constraint leads to stricter requirements than simply imposing locality, in the form of bilocality inequalities. In this work we consider a natural generalization of the bilocality scenario; namely, the star network consisting of a single central party surrounded by n edge parties, each of which shares an independent source with the center. We derive inequalities which are satisfied by all local correlations in this scenario, for the cases when the central party performs (i) two dichotomic measurements (ii) a single Bell-state measurement. We demonstrate quantum violations of these inequalities and study both the robustness to noise and to losses.
Nature Commun.

Work extraction and thermodynamics for individual quantum systems

P. Skrzypczyk, A. J. Short, S. Popescu

Nature Commun. 5, 4185 (2014)

Abstract Full Text

Thermodynamics is traditionally concerned with systems comprised of a large number of particles. Here we present a framework for extending thermodynamics to individual quantum systems, including explicitly a thermal bath and work-storage device (essentially a ‘weight’ that can be raised or lowered). We prove that the second law of thermodynamics holds in our framework, and gives a simple protocol to extract the optimal amount of work from the system, equal to its change in free energy. Our results apply to any quantum system in an arbitrary initial state, in particular including non-equilibrium situations. The optimal protocol is essentially reversible, similar to classical Carnot cycles, and indeed, we show that it can be used to construct a quantum Carnot engine.
Phys. Rev. Lett.

Quantifying Einstein-Podolsky-Rosen Steering

P. Skrzypczyk, M. Navascués, D. Cavalcanti

Phys. Rev. Lett. 112, 180404 (2014)

Abstract Full Text

Einstein-Podolsky-Rosen steering is a form of bipartite quantum correlation that is intermediate between entanglement and Bell nonlocality. It allows for entanglement certification when the measurements performed by one of the parties are not characterized (or are untrusted) and has applications in quantum key distribution. Despite its foundational and applied importance, Einstein-Podolsky-Rosen steering lacks a quantitative assessment. Here we propose a way of quantifying this phenomenon and use it to study the steerability of several quantum states. In particular, we show that every pure entangled state is maximally steerable and the projector onto the antisymmetric subspace is maximally steerable for all dimensions; we provide a new example of one-way steering and give strong support that states with positive-partial transposition are not steerable.
Phys. Rev. E

Entanglement enhances cooling in microscopic quantum refrigerators

N. Brunner, M. Huber, N. Linden, S. Popescu, R. Silva, P. Skrzypczyk

Phys. Rev. E 89, 032115 (2014)

Abstract Full Text

Small self-contained quantum thermal machines function without external source of work or control but using only incoherent interactions with thermal baths. Here we investigate the role of entanglement in a small self-contained quantum refrigerator. We first show that entanglement is detrimental as far as efficiency is concerned—fridges operating at efficiencies close to the Carnot limit do not feature any entanglement. Moving away from the Carnot regime, we show that entanglement can enhance cooling and energy transport. Hence, a truly quantum refrigerator can outperform a classical one. Furthermore, the amount of entanglement alone quantifies the enhancement in cooling.

2013

New J. Phys.

Quantum Cheshire Cats

Y. Aharonov, S. Popescu, D. Rohrlich, P. Skrzypczyk

New J. Phys. 15, 113015 (2013)

Abstract Full Text

In this paper we present a quantum Cheshire Cat. In a pre- and post-selected experiment we find the Cat in one place, and its grin in another. The Cat is a photon, while the grin is its circular polarization.

2012

Phys. Rev. E APS Viewpoint

Virtual qubits, virtual temperatures, and the foundations of thermodynamics

N. Brunner, N. Linden, S. Popescu, P. Skrzypczyk

Phys. Rev. E 85, 051117 (2012)

Abstract Full Text

We argue that thermal machines can be understood from the perspective of “virtual qubits” at “virtual temperatures”: The relevant way to view the two heat baths which drive a thermal machine is as a composite system. Virtual qubits are two-level subsystems of this composite, and their virtual temperatures can take on any value, positive or negative. Thermal machines act upon an external system by placing it in thermal contact with a well-selected range of virtual qubits and temperatures. We demonstrate these claims by studying the smallest thermal machines. We show further that this perspective provides a powerful way to view thermodynamics, by analyzing a number of phenomena. This includes approaching Carnot efficiency (where we find that all machines do so essentially by becoming equivalent to the smallest thermal machines), entropy production in irreversible machines, and a way to view work in terms of negative temperature and population inversion. Moreover we introduce the idea of “genuine” thermal machines and are led to considering the concept of “strength” of work.

2011

Phys. Rev. A

Large violation of Bell inequalities using both particle and wave measurements

D. Cavalcanti, N. Brunner, P. Skrzypczyk, A. Salles, V. Scarani

Phys. Rev. A 84, 022105 (2011)

Abstract Full Text

When separated measurements on entangled quantum systems are performed, the theory predicts correlations that cannot be explained by any classical mechanism: communication is excluded because the signal should travel faster than light; preestablished agreement is excluded because Bell inequalities are violated. All optical demonstrations of such violations have involved discrete degrees of freedom and are plagued by the detection-efficiency loophole. A promising alternative is to use continuous variables combined with highly efficient homodyne measurements. However, all the schemes proposed so far use states or measurements that are extremely difficult to achieve, or they produce very weak violations. We present a simple method to generate large violations for feasible states using both photon counting and homodyne detections. The present scheme can also be used to obtain nonlocality from easy-to-prepare Gaussian states (e.g., two-mode squeezed state).
J. Phys. A: Math. Theor.

The smallest refrigerators can reach maximal efficiency

P. Skrzypczyk, N. Brunner, N. Linden, S. Popescu

J. Phys. A: Math. Theor. 44, 492002 (2011)

Abstract Full Text

We investigate whether size imposes a fundamental constraint on the efficiency of small thermal machines. We analyse in detail a model of a small self-contained refrigerator consisting of three qubits. We show analytically that this system can reach the Carnot efficiency, thus demonstrating that there exists no complementarity between size and efficiency.
J. Phys. A: Math. Theor.

Physics within a quantum reference frame

R. M. Angelo, N. Brunner, S. Popescu, A. J. Short, P. Skrzypczyk

J. Phys. A: Math. Theor. 44, 145304 (2011)

Abstract Full Text

We investigate the physics of quantum reference frames. Specifically, we study several simple scenarios involving a small number of quantum particles, whereby we promote one of these particles to the role of a quantum observer and ask what is the description of the rest of the system, as seen by this observer? We highlight the interesting aspects of such questions by presenting a number of apparent paradoxes. By unravelling these paradoxes, we obtain a better understanding of the physics of quantum reference frames.
Phys. Rev. Lett.

Bound Nonlocality and Activation

N. Brunner, D. Cavalcanti, A. Salles, P. Skrzypczyk

Phys. Rev. Lett. 106, 020402 (2011)

Abstract Full Text

We investigate nonlocality distillation using measures of nonlocality based on the Elitzur-Popescu-Rohrlich decomposition. For a certain number of copies of a given nonlocal box, we define two quantities of interest: (i) the nonlocal cost and (ii) the distillable nonlocality. We find that there exist boxes whose distillable nonlocality is strictly smaller than their nonlocal cost. Thus nonlocality displays a form of irreversibility which we term “bound nonlocality.” Finally, we show that nonlocal distillability can be activated.

2010

Phys. Rev. Lett.

How Small Can Thermal Machines Be? The Smallest Possible Refrigerator

N. Linden, S. Popescu, P. Skrzypczyk

Phys. Rev. Lett. 105, 130401 (2010)

Abstract Full Text

We investigate the fundamental dimensional limits to thermodynamic machines. In particular, we show that it is possible to construct self-contained refrigerators (i.e., not requiring external sources of work) consisting of only a small number of qubits and/or qutrits. We present three different models, consisting of two qubits, a qubit and a qutrit with nearest-neighbor interactions, and a single qutrit, respectively. We then investigate the fundamental limits to their performance; in particular, we show that it is possible to cool towards absolute zero.

2009

Phys. Rev. A

Closed sets of nonlocal correlations

J. Allcock, N. Brunner, N. Linden, S. Popescu, P. Skrzypczyk, T. Vértesi

Phys. Rev. A 80, 062107 (2009)

Abstract Full Text

We present a fundamental concept—closed sets of correlations—for studying nonlocal correlations. We argue that sets of correlations corresponding to information-theoretic principles, or more generally to consistent physical theories, must be closed under a natural set of operations. Hence, studying the closure of sets of correlations gives insight into which information-theoretic principles are genuinely different, and which are ultimately equivalent. This concept also has implications for understanding why quantum nonlocality is limited, and for finding constraints on physical theories beyond quantum
New J. Phys.

Couplers for non-locality swapping

P. Skrzypczyk, N. Brunner

New J. Phys. 11, 073014 (2009)

Abstract Full Text

Studying generalized non-signaling theories brings insight into the foundations of quantum mechanics. Here we focus on a dynamical process in such general theories, namely non-locality swapping, the analogue of quantum entanglement swapping. In order to implement such a protocol, one needs to define a coupler, which performs the equivalent of quantum joint measurements on generalized ‘box-like’ states. Establishing a connection to Bell inequalities, we define consistent couplers for theories containing an arbitrary amount of non-locality, which leads us to introduce the concepts of perfect and minimal couplers. Remarkably, Tsirelson’s bound for quantum non-locality naturally appears in our study.
Phys. Rev. Lett.

Nonlocality Distillation and Postquantum Theories with Trivial Communication Complexity

N. Brunner, P. Skrzypczyk

Phys. Rev. Lett. 102, 160403 (2009)

Abstract Full Text

We first present a protocol for deterministically distilling nonlocality, building upon a recent result of Forster et al. [Phys. Rev. Lett. 102, 120401 (2009)]. Our protocol, which is optimal for two-copy distillation, works efficiently for a specific class of postquantum nonlocal boxes, which we term correlated nonlocal boxes. In the asymptotic limit, all correlated nonlocal boxes are distilled to the maximally nonlocal box of Popescu and Rohrlich. Then, taking advantage of a result of Brassard et al. [Phys. Rev. Lett. 96, 250401 (2006)] we show that all correlated nonlocal boxes make communication complexity trivial, and therefore appear very unlikely to exist in nature. Astonishingly, some of these nonlocal boxes are arbitrarily close to the set of classical correlations. This result therefore gives new insight to the problem of why quantum nonlocality is limited.
Phys. Rev. Lett.

Emergence of Quantum Correlations from Nonlocality Swapping

P. Skrzypczyk, N. Brunner, S. Popescu

Phys. Rev. Lett. 102, 110402 (2009)

Abstract Full Text

By studying generalized nonsignaling theories, the hope is to find out what makes quantum mechanics so special. In the present Letter, we revisit the paradigmatic model of nonsignaling boxes and introduce the concept of a genuine box. This will allow us to present the first generalized nonsignaling model featuring quantumlike dynamics. In particular, we present the coupler, a device enabling nonlocality swapping, the analogue of quantum entanglement swapping, as well as teleportation. Remarkably, part of the boundary between quantum and post-quantum correlations emerges in our study.