arXiv subjects

Paul Skrzypczyk

Publications and source records attributed to Paul Skrzypczyk.

At least 37 records · Page 2Linked to original sources

arXiv2023

Fundamental connections between utility theories of wealth and information theory

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.

cs.IT↗

arXiv2021

Characterisation of quantum betting tasks in terms of Arimoto mutual information

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 $α\rightarrow \infty$, and quantum state (channel) exclusion when $α\rightarrow -\infty$. 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.

quant-ph↗

arXiv2021

Network Quantum Steering

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 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.

quant-ph↗

arXiv2021

Catalytic quantum teleportation and beyond

We address fundamental limitations of quantum teleportation -- the process of transferring quantum information using classical communication and preshared entanglement. We develop a new teleportation protocol based upon the idea of using ancillary entanglement catalytically, i.e. without depleting it. This protocol is then used to show that catalytic entanglement allows for a noiseless quantum channel to be simulated with a quality that could never be achieved using only entanglement from the shared state, even for catalysts with a small dimension. On the one hand, this allows for a more faithful transmission of quantum information using generic states and a fixed amount of consumed entanglement. On the other hand, this shows, for the first time, that entanglement catalysis provides a genuine advantage in a generic quantum-information processing task. Finally, we show that similar ideas can be directly applied to study quantum catalysis for more general problems in quantum mechanics. As an application, we show that catalysts can activate so-called passive states, a concept that finds widespread application e.g. in quantum thermodynamics.

quant-ph↗

arXiv2021

All states are universal catalysts in quantum thermodynamics

Quantum catalysis is a fascinating concept which demonstrates that 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 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 multi-copy 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 but 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 multi-copy form nor a very large dimension catalyst are required to activate most allowed transformations catalytically.

quant-ph↗

arXiv2020

The operational significance of the quantum resource theory of Buscemi nonlocality

Although entanglement is necessary for observing nonlocality in a Bell experiment, there are entangled states which can never be used to demonstrate nonlocal correlations. In a seminal paper [PRL 108, 200401 (2012)] F. Buscemi 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 establish its operational significance. In particular, we show that any distributed measurement which can demonstrate Buscemi nonlocal correlations provides strictly better performance than any distributed measurement which does not use entanglement in the task of distributed state discrimination. We also show that the maximal amount of Buscemi nonlocality that can be generated using a given state is precisely equal to its entanglement content. Finally, we prove a quantitative relationship between: Buscemi nonlocality, the ability to perform nonclassical teleportation, and entanglement. Using this relationship we propose new discrimination tasks for which nonclassical teleportation and entanglement lead to an advantage over their classical counterparts.

quant-ph↗

arXiv2020

Bipartite post-quantum steering in generalised scenarios

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 post-quantum steering is a genuinely new type of post-quantum nonlocality, which does not follow from post-quantum Bell nonlocality. In addition, we present a method to bound quantum violations of steering inequalities in these scenarios.

quant-ph↗

arXiv2020

Multi-object operational tasks for convex quantum resource theories

The prevalent modus operandi within the framework of quantum resource theories has been to characterise and harness the resources within single objects, in what we can call \emph{single-object} quantum resource theories. One can wonder however, whether the resources contained within multiple different types of objects, now in a \emph{multi-object} quantum resource theory, can simultaneously be exploited for the benefit of an operational task. In this work, we introduce examples of such multi-object operational tasks in the form of subchannel discrimination and subchannel exclusion games, in which the player harnesses the resources contained within 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 for which classical post-processing is a free operation. Furthermore, we prove that the advantage in these multi-object operational tasks is determined, in a multiplicative manner, by the resource quantifiers of: \emph{generalised robustness of resource} of both state and measurement for discrimination games and \emph{weight of resource} of both state and measurement for exclusion games.

quant-ph↗

arXiv2020

Device-independent quantum key distribution with single-photon sources

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.

quant-ph↗

arXiv2020

Quantifying measurement incompatibility of mutually unbiased bases

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 (given $d$ is 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.

quant-ph↗

arXiv2020

The operational advantages provided by non-classical teleportation

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 non-classical 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 entangled 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 upon the notion of teleportation simulation, one classical, and one quantum.

quant-ph↗

arXiv2019

Exploring the limits of no backward in time signalling

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

quant-ph↗

arXiv2019

Operational interpretation of weight-based resource quantifiers in convex quantum resource theories of states

We introduce the resource quantifier of weight of resource for convex quantum resource theories of states with arbitrary resources. We show that it captures the advantage that a resourceful state offers over all possible free states, in the operational task of exclusion of subchannels. Furthermore, we introduce information-theoretic quantities related to exclusion and find a connection between the weight of resource of a state, and the exclusion-type information of ensembles it can generate. These results provide support to a recent conjecture made in the context of convex quantum resource theories of measurements, about the existence of a weight-exclusion correspondence whenever there is a robustness-discrimination one. The results found in this article 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.

quant-ph↗

arXiv2019

Weight of informativeness, state exclusion games and excludible information

We consider the quantum resource theory of measurement informativeness and introduce a weight-based quantifier of informativeness. We show that this quantifier has operational significance from the perspective of quantum state exclusion, by showing that it precisely captures the advantage a measurement provides in minimising the error in this game. We furthermore introduce information theoretic quantities related to exclusion, in particular the notion of excludible information of a quantum channel, and show that for the case of quantum-to-classical channels it is determined precisely by the weight of informativeness. This establishes a three-way correspondence which sits in parallel to the recently discovered correspondence in quantum resource theories between robustness-based quantifiers, discrimination games, and accessible information. We conjecture that the new correspondence between a weight-based quantifier and an exclusion-based task found in this work is a generic correspondence that holds in the context of quantum resource theories.

quant-ph↗

arXiv2019

The complexity of compatible measurements

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 -- 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 doesn't trivialise 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.

quant-ph↗

arXiv2019

All sets of incompatible measurements give an advantage in quantum state discrimination

Some quantum measurements can not 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 later with quantum state discrimination.

quant-ph↗

arXiv2018

Robustness of Measurement, discrimination games and accessible information

We introduce a way of quantifying how informative a quantum measurement is, starting from a resource-theoretic perspective. This quantifier, which we call the robustness of measurement, 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 an suitably chosen state discrimination game. We further show that it is the single-shot generalisation of the accessible information of a certain quantum-to-classical channel. Using this insight, we also show that the recently-introduced robustness of coherence is the single-shot generalisation of the accessible information of an ensemble. Finally we discuss more generally the connection between robustness-based measures, discrimination problems and single-shot information theory.

quant-ph↗

arXiv2018

Estimating entanglement in teleportation experiments

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 in teleportation experiments. We show that the data accessible in a teleportation experiment allows 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.

quant-ph↗