arXiv subjects

Beata Zjawin

Publications and source records attributed to Beata Zjawin.

9 recordsLinked to original sources

arXiv2026

Typicality of Contextuality

Identifying when observed statistics cannot be explained by any reasonable classical model is a central problem in quantum foundations. A principled and universally applicable approach to defining and identifying nonclassicality is given by the notion of generalized noncontextuality. Here, we study the typicality of contextuality -- namely, the likelihood that randomly chosen quantum preparations and measurements produce nonclassical statistics. Using numerical linear programs to test for the existence of a generalized-noncontextual model, we find that contextuality is fairly common: even in experiments with only a modest number of random preparations and measurements, contextuality arises with probability over 99%. We also show that while typicality of contextuality decreases as the purity (sharpness) of the preparations (measurements) decreases, this dependence is not especially pronounced, so contextuality is fairly typical even in settings with realistic noise. Finally, we show that although nonzero contextuality is quite typical, quantitatively high degrees of contextuality are not as typical, and so large quantum advantages (like for parity-oblivious multiplexing, which we take as a case study) are not as typical. We provide an open-source toolbox that outputs the typicality of contextuality as a function of tunable parameters (such as lower and upper bounds on purity and other constraints on states and measurements). This toolbox can inform the design of experiments that achieve the desired typicality of contextuality for specified experimental constraints.

quant-ph↗

arXiv2026

The resource theory of causal influence and knowledge of causal influence

Understanding and quantifying causal relationships between variables is essential for reasoning about the physical world. In this work, we develop a resource-theoretic framework to do so. Here, we focus on the simplest nontrivial setting -- two variables that are causally ordered, meaning that the first has the potential to influence the second, without hidden confounding. First, we introduce the resource theory that directly quantifies causal influence of a functional dependence in this setting and show that the problem of deciding convertibility of resources and identifying a complete set of monotones has a relatively straightforward solution. Following this, we introduce the resource theory that arises naturally when one has uncertainty about the functional dependence. We describe a linear program for deciding the question of whether one resource (i.e., state of knowledge about the functional dependence) can be converted to another. Then, we focus on the case where the variables are binary. In this case, we identify a triple of monotones that are complete in the sense that they capture the partial order over the set of all resources, and we provide an interpretation of each.

math.ST↗

arXiv2025

Robust self-testing of quantum steering assemblages via operator inequalities

Robust self-testing provides a framework for certifying quantum resources under experimental imperfections. Improving robustness bounds for quantum resources such as quantum states, steering assemblages, and measurements is a constant effort that ensures relevance in the experimental realm. Despite progress in analytic self-testing methods for quantum states and measurements, extending these techniques to device-independent certification of steering assemblages has remained an open challenge, with previous work relying primarily on numerical approaches. We address this gap by developing operator inequalities for robust self-testing of quantum steering assemblages. Specifically, we consider the assemblage that achieves maximal violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality and obtain explicit lower bounds on its certification fidelity. Our analytic approach yields results that significantly improve upon previous numerical bounds, representing the first analytic treatment of device-independent assemblage self-testing. This work demonstrates a new application of operator inequalities beyond quantum state certification and contributes to the foundational understanding of device-independent certification in steering scenarios, potentially guiding future theoretical and experimental developments.

quant-ph↗

arXiv2024

Activation of post-quantumness in bipartite generalised EPR scenarios

In a standard bipartite Einstein-Podolsky-Rosen (EPR) scenario, Alice and Bob share a system prepared in an entangled state and Alice performs local measurements. One possible generalisation of this set-up is to allow Bob to also locally process his subsystem. Then, correlations generated in such generalised EPR scenarios are examples of non-signalling bipartite resources, called assemblages, that can exhibit post-quantum behavior, i.e., cannot be generated using solely quantum systems. There exist assemblages that, despite being post-quantum resources, can only generate quantum correlations in bipartite Bell-type scenarios. Here, we present a protocol for activation of post-quantumness in bipartite generalised EPR scenarios such as the so-called Bob-with-input, measurement-device-independent, and channel EPR scenarios. By designing a protocol that involves distributing the assemblages in a larger network, we derive tailored Bell inequalities which can be violated beyond their quantum bound in this new set-up. Our results show that in all of the above generalised scenarios, the post-quantumness of the assemblages can be witnessed at the level of correlations they produce.

quant-ph↗

arXiv2023

The resource theory of nonclassicality of channel assemblages

When two parties, Alice and Bob, share correlated quantum systems and Alice performs local measurements, Alice's updated description of Bob's state can provide evidence of nonclassical correlations. This simple scenario, famously introduced by Einstein, Podolsky and Rosen (EPR), can be modified by allowing Bob to also have a classical or quantum system as an input. In this case, Alice updates her knowledge of the channel (rather than of a state) in Bob's lab. In this paper, we provide a unified framework for studying the nonclassicality of various such generalizations of the EPR scenario. We do so using a resource theory wherein the free operations are local operations and shared randomness (LOSR). We derive a semidefinite program for studying the pre-order of EPR resources and discover possible conversions between the latter. Moreover, we study conversions between post-quantum resources both analytically and numerically.

quant-ph↗

arXiv2023

Engineering the sensitivity of macroscopic physical systems to variations in the fine-structure constant

Experiments aimed at searching for variations in the fine-structure constant $α$ are based on spectroscopy of transitions in microscopic bound systems, such as atoms and ions, or resonances in optical cavities. The sensitivities of these systems to variations in $α$ are typically on the order of unity and are fixed for a given system. For heavy atoms, highly charged ions and nuclear transitions, the sensitivity can be increased by benefiting from the relativistic effects and favorable arrangement of quantum states. This article proposes a new method for controlling the sensitivity factor of macroscopic physical systems. Specific concepts of optical cavities with tunable sensitivity to $α$ are described. These systems show qualitatively different properties from those of previous studies of the sensitivity of macroscopic systems to variations in $α$, in which the sensitivity was found to be fixed and fundamentally limited to an order of unity. Although possible experimental constraints attainable with the specific optical cavity arrangements proposed in this article do not yet exceed the present best constraints on $α$ variations, this work paves the way for developing new approaches to searching for variations in the fundamental constants of physics.

physics.atom-ph↗

arXiv2023

Entropic Inequality Constraints from $e$-separation Relations in Directed Acyclic Graphs with Hidden Variables

Directed acyclic graphs (DAGs) with hidden variables are often used to characterize causal relations between variables in a system. When some variables are unobserved, DAGs imply a notoriously complicated set of constraints on the distribution of observed variables. In this work, we present entropic inequality constraints that are implied by $e$-separation relations in hidden variable DAGs with discrete observed variables. The constraints can intuitively be understood to follow from the fact that the capacity of variables along a causal pathway to convey information is restricted by their entropy; e.g. at the extreme case, a variable with entropy $0$ can convey no information. We show how these constraints can be used to learn about the true causal model from an observed data distribution. In addition, we propose a measure of causal influence called the minimal mediary entropy, and demonstrate that it can augment traditional measures such as the average causal effect.

stat.ML↗

arXiv2023

Quantifying EPR: the resource theory of nonclassicality of common-cause assemblages

Einstein-Podolsky-Rosen (EPR) steering is often (implicitly or explicitly) taken to be evidence for spooky action-at-a-distance. An alternative perspective on steering is that Alice has no causal influence on the physical state of Bob's system; rather, Alice merely updates her knowledge of the state of Bob's system by performing a measurement on a system correlated with his. In this work, we elaborate on this perspective (from which the very term 'steering' is seen to be inappropriate), and we are led to a resource-theoretic treatment of correlations in EPR scenarios. For both bipartite and multipartite scenarios, we develop the resulting resource theory, wherein the free operations are local operations and shared randomness (LOSR). We show that resource conversion under free operations in this paradigm can be evaluated with a single instance of a semidefinite program, making the problem numerically tractable. Moreover, we find that the structure of the pre-order of resources features interesting properties, such as infinite families of incomparable resources. In showing this, we derive new EPR resource monotones. We also discuss advantages of our approach over a pre-existing proposal for a resource theory of 'steering', and discuss how our approach sheds light on basic questions, such as which multipartite assemblages are classically explainable.

quant-ph↗

arXiv2021

Restricted Hidden Cardinality Constraints in Causal Models

Causal models with unobserved variables impose nontrivial constraints on the distributions over the observed variables. When a common cause of two variables is unobserved, it is impossible to uncover the causal relation between them without making additional assumptions about the model. In this work, we consider causal models with a promise that unobserved variables have known cardinalities. We derive inequality constraints implied by d-separation in such models. Moreover, we explore the possibility of leveraging this result to study causal influence in models that involve quantum systems.

math.ST↗