Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2208.13976 · Physical Review Letters

Distilling Nonlocality in Quantum Correlations

Sahil Gopalkrishna Naik, Govind Lal Sidhardh, Samrat Sen, Arup Roy, Ashutosh Rai, Manik Banik

Published Jun 1, 2023• 11 citations
arXivHTMLPDF

Abstract

Nonlocality, as established by the seminal Bell's theorem, is considered to be the most striking feature of correlations present in spacelike separated events. Its practical application in device independent protocols, such as secure key distribution, randomness certification, etc., demands identification and amplification of such correlations observed in the quantum world. In this Letter we study the prospect of nonlocality distillation, wherein, by applying a natural set of free operations (called wirings) on many copies of weakly nonlocal systems, one aims to generate correlations of higher nonlocal strength. In the simplest Bell scenario, we identify a protocol, namely, logical OR-AND wiring, that can distill nonlocality to a significantly high degree starting from arbitrarily weak quantum nonlocal correlations. As it turns out, our protocol has several interesting facets: (i) it demonstrates that a set of distillable quantum correlations has nonzero measure in the full eight-dimensional correlation space, (ii) it can distill quantum Hardy correlations by preserving its structure, (iii) it shows that (nonlocal) quantum correlations sufficiently close to the local deterministic points can be distilled by a significant amount. Finally, we also demonstrate efficacy of the considered distillation protocol in detecting postquantum correlations.

DOI
10.1103/physrevlett.130.220201

Related papers

Advantages of Multicopy Nonlocality Distillation and Its Application to Minimizing Communication Complexity

Giorgos Eftaxias, Mirjam Weilenmann, Roger Colbeck

Nonlocal correlations are a central feature of quantum theory, and understanding why quantum theory has a limited amount of nonlocality is a fundamental problem. Since nonlocality also has technological applications, e.g., for device-independent cryptography, it is useful to understand it as a resource and, in particular, whether and how different types of nonlocality can be interconverted. Here we focus on nonlocality distillation which involves using several copies of a nonlocal resource to generate one with more nonlocality. We introduce several distillation schemes which distill an extended part of the set of nonlocal correlations including quantum correlations. Our schemes are based on a natural set of operational procedures known as wirings that can be applied regardless of the underlying theory. Some are sequential algorithms that repeatedly use a two-copy protocol, while others are genuine three-copy distillation protocols. In some regions we prove that genuine three-copy protocols are strictly better than two-copy protocols. By applying our new protocols we also increase the region in which nonlocal correlations are known to give rise to trivial communication complexity. This brings us closer to an understanding of the sets of nonlocal correlations that can be recovered from information-theoretic principles, which, in turn, enhances our understanding of what is special about quantum theory.

arXiv:2206.02817•Physical Review Letters•Mar 6, 2023•11 citations

Extending loophole-free nonlocal correlations to arbitrarily large distances

Anubhav Chaturvedi, Giuseppe Viola, Marcin Pawłowski

Abstract One of the most striking features of quantum theory is that it allows spatially separated observers to share correlations that resist local-causal (classical) explanations, a phenomenon referred to as Bell nonlocality[1, 2]. Besides their foundational relevance, the nonlocal correlations enable distant observers to accomplish classically inconceivable information processing and cryptographic feats such as unconditionally secure device-independent key distribution schemes[3-5]. However, the distances over which nonlocal correlations can be realized in state-of-the-art Bell experiments remain severely limited owing to the high threshold efficiencies of the detectors and the fragility of the nonlocal correlations to experimental noise[6, 7]. Instead of looking for quantum strategies with marginally lower threshold requirements, we exploit the properties of loophole-free nonlocal correlations, which are experimentally attainable today, albeit at short distances, to extend them over arbitrarily large distances. Specifically, we consider Bell experiments wherein the spatially separated parties randomly choose the location of their measurement devices in addition to their measurement settings. We demonstrate that when devices close to the entanglement source are perfect and witness extremal loophole-free nonlocal correlations, such correlations can be extended to devices placed arbitrarily far from the source, with almost zero detection efficiency and visibility. To accommodate imperfections close to the source, we demonstrate a specific analytical tradeoff: the higher the loophole-free nonlocality close to the source, the lower the threshold requirements away from the source. We utilize this analytical tradeoff paired with optimal quantum strategies to estimate the critical requirements of a measurement device placed away from the source in the simplest non-trivial scenario and formulate a versatile numerical method applicable to generic network scenarios. Our results demonstrate that the properties of already feasible short-distance loophole-free nonlocal correlations can be exploited to extend them to longer distances, enabling device-independent information processing and cryptography fuelled by long-distance loophole-free nonlocal correlations to become near-term commonplace technologies.

arXiv:2211.14231•npj Quantum Information•Jan 11, 2024•12 citations

Quantum Nonlocality: Multicopy Resource Interconvertibility and Their Asymptotic Inequivalence

Subhendu B. Ghosh, Snehasish Roy Chowdhury, Guruprasad Kar +3 more

Quantum nonlocality, pioneered in Bell's seminal work and subsequently verified through a series of experiments, has drawn substantial attention due to its practical applications in various protocols. Evaluating and comparing the extent of nonlocality within distinct quantum correlations holds significant practical relevance. Within the resource theoretic framework this can be achieved by assessing the interconversion rate among different nonlocal correlations under free local operations and shared randomness. In this study we, however, present instances of quantum nonlocal correlations that are incomparable in the strongest sense. Specifically, when starting with an arbitrary many copies of one nonlocal correlation, it becomes impossible to obtain even a single copy of the other correlation, and this incomparability holds in both directions. Such incomparable quantum correlations can be obtained even in the simplest Bell scenario, which involves two parties, each having two dichotomic measurements setups. Notably, there exist an uncountable number of such incomparable correlations. Our result challenges the notion of a "unique gold coin," often referred to as the "maximally resourceful state," within the framework of the resource theory of quantum nonlocality. To this end, we provide examples of isotropic quantum correlations that cannot be distilled up to the Tsirelson point, and thus partially answer a long-standing open question in nonlocality distillation.

arXiv:2310.16386•Physical Review Letters•Jun 21, 2024•7 citations

Nonlocality distillation and quantum voids

Samuraí Brito, George Moreno, Ashutosh Rai +1 more

Via nonlocality distillation, a number of copies of a given nonlocal correlation can be turned into a new correlation displaying a higher degree of nonlocality. Apart from its clear relevance in situations where nonlocality is a resource, distillation protocols also play an important role in the understanding of information-theoretical principles for quantum theory. Here, we derive a necessary condition for nonlocality distillation from two copies and apply it, among other results, to show that one-dimensional ($1\mathrm{D}$) and $2\mathrm{D}$ quantum voids---faces of the nonlocal simplex set with no quantum realization---can be distilled up to PR boxes. With that, we generalize previous results in the literature, for instance, showing a broad class of postquantum correlations that make communication complexity trivial and violate the information causality principle.

arXiv:1903.09289•Physical Review A•Jul 1, 2019•9 citations

Quantum Correlations: From Full Nonlocality to Device-Independent Certification

Edwin Peter Lobo

Quantum theory admits correlations between distant parties that are stronger than those permitted by classical physics. Such correlations, which are termed nonlocal, have been studied extensively since their discovery by John Bell in 1964. This thesis makes progress on various aspects of quantum nonlocality both from a foundational and practical perspective. We begin by studying a foundational question on the relationship between nonlocality and quantum entanglement. We show that the strongest form of nonlocality, also called pseudo-telepathy or full nonlocality, can be demonstrated by non-maximally entangled states and prove that all pure entangled states can demonstrate full nonlocality in the many-copy scenario. We also provide non-trivial examples of fully nonlocal mixed states. We then turn to the study of another phenomenon in quantum theory which is essential in almost all demonstrations of non-classicality—measurement incompatibility. We generalise the notion of measurement incompatibility and show that our notion has strong operational relevance: it captures the randomness in the outcomes of an untrusted measurement device against a classical adversary. We use our formalism to derive new bounds on the experimental losses and noise that can be tolerated in quantum communication protocols before they become insecure. We then begin a systematic study of routed Bell experiments, a variant of standard Bell experiments that was introduced to demonstrate nonlocality over long distances in the presence of losses and noise. We formalize the notion of genuine long-range quantum correlations in routed Bell experiments and develop numerical and analytical tools to characterize them. We show that routed Bell experiments allow for the demonstration of long-range quantum correlations at arbitrarily large distances using only entangled qubit states. We then prove the security of fully device-independent (DI) quantum key distribution (QKD) protocols based on routed Bell tests and quantify the resulting improvement in key rate and distance compared to standard DI QKD protocols.

•Sep 1, 2026•0 citations

Nonlocality Distillation and Postquantum Theories with Trivial Communication Complexity

Nicolas Brunner, Paul Skrzypczyk

We first present a protocol for deterministically distilling nonlocality, building upon a recent result of Forster et al. [Phys. Rev. Lett. 102, 120401 (2009)10.1103/PhysRevLett.102.120401]. 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)10.1103/PhysRevLett.96.250401] 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.

arXiv:0901.4070•Physical Review Letters•Apr 24, 2009•118 citations
Nonlocality, as established by the seminal Bell's theorem, is considered to be the most striking feature of correlations present in spacelike separated events. Its practical application in device independent protocols, such as secure key distribution, randomness certification, etc., demands identification and amplification of such correlations observed in the quantum world. In this Letter we study the prospect of nonlocality distillation, wherein, by applying a natural set of free operations (called wirings) on many copies of weakly nonlocal systems, one aims to generate correlations of higher nonlocal strength. In the simplest Bell scenario, we identify a protocol, namely, logical OR-AND wiring, that can distill nonlocality to a significantly high degree starting from arbitrarily weak quantum nonlocal correlations. As it turns out, our protocol has several interesting facets: (i) it demonstrates that a set of distillable quantum correlations has nonzero measure in the full eight-dimensional correlation space, (ii) it can distill quantum Hardy correlations by preserving its structure, (iii) it shows that (nonlocal) quantum correlations sufficiently close to the local deterministic points can be distilled by a significant amount. Finally, we also demonstrate efficacy of the considered distillation protocol in detecting postquantum correlations.
Nonlocal correlations are a central feature of quantum theory, and understanding why quantum theory has a limited amount of nonlocality is a fundamental problem. Since nonlocality also has technological applications, e.g., for device-independent cryptography, it is useful to understand it as a resource and, in particular, whether and how different types of nonlocality can be interconverted. Here we focus on nonlocality distillation which involves using several copies of a nonlocal resource to generate one with more nonlocality. We introduce several distillation schemes which distill an extended part of the set of nonlocal correlations including quantum correlations. Our schemes are based on a natural set of operational procedures known as wirings that can be applied regardless of the underlying theory. Some are sequential algorithms that repeatedly use a two-copy protocol, while others are genuine three-copy distillation protocols. In some regions we prove that genuine three-copy protocols are strictly better than two-copy protocols. By applying our new protocols we also increase the region in which nonlocal correlations are known to give rise to trivial communication complexity. This brings us closer to an understanding of the sets of nonlocal correlations that can be recovered from information-theoretic principles, which, in turn, enhances our understanding of what is special about quantum theory.
Abstract One of the most striking features of quantum theory is that it allows spatially separated observers to share correlations that resist local-causal (classical) explanations, a phenomenon referred to as Bell nonlocality[1, 2]. Besides their foundational relevance, the nonlocal correlations enable distant observers to accomplish classically inconceivable information processing and cryptographic feats such as unconditionally secure device-independent key distribution schemes[3-5]. However, the distances over which nonlocal correlations can be realized in state-of-the-art Bell experiments remain severely limited owing to the high threshold efficiencies of the detectors and the fragility of the nonlocal correlations to experimental noise[6, 7]. Instead of looking for quantum strategies with marginally lower threshold requirements, we exploit the properties of loophole-free nonlocal correlations, which are experimentally attainable today, albeit at short distances, to extend them over arbitrarily large distances. Specifically, we consider Bell experiments wherein the spatially separated parties randomly choose the location of their measurement devices in addition to their measurement settings. We demonstrate that when devices close to the entanglement source are perfect and witness extremal loophole-free nonlocal correlations, such correlations can be extended to devices placed arbitrarily far from the source, with almost zero detection efficiency and visibility. To accommodate imperfections close to the source, we demonstrate a specific analytical tradeoff: the higher the loophole-free nonlocality close to the source, the lower the threshold requirements away from the source. We utilize this analytical tradeoff paired with optimal quantum strategies to estimate the critical requirements of a measurement device placed away from the source in the simplest non-trivial scenario and formulate a versatile numerical method applicable to generic network scenarios. Our results demonstrate that the properties of already feasible short-distance loophole-free nonlocal correlations can be exploited to extend them to longer distances, enabling device-independent information processing and cryptography fuelled by long-distance loophole-free nonlocal correlations to become near-term commonplace technologies.
Quantum nonlocality, pioneered in Bell's seminal work and subsequently verified through a series of experiments, has drawn substantial attention due to its practical applications in various protocols. Evaluating and comparing the extent of nonlocality within distinct quantum correlations holds significant practical relevance. Within the resource theoretic framework this can be achieved by assessing the interconversion rate among different nonlocal correlations under free local operations and shared randomness. In this study we, however, present instances of quantum nonlocal correlations that are incomparable in the strongest sense. Specifically, when starting with an arbitrary many copies of one nonlocal correlation, it becomes impossible to obtain even a single copy of the other correlation, and this incomparability holds in both directions. Such incomparable quantum correlations can be obtained even in the simplest Bell scenario, which involves two parties, each having two dichotomic measurements setups. Notably, there exist an uncountable number of such incomparable correlations. Our result challenges the notion of a "unique gold coin," often referred to as the "maximally resourceful state," within the framework of the resource theory of quantum nonlocality. To this end, we provide examples of isotropic quantum correlations that cannot be distilled up to the Tsirelson point, and thus partially answer a long-standing open question in nonlocality distillation.
Via nonlocality distillation, a number of copies of a given nonlocal correlation can be turned into a new correlation displaying a higher degree of nonlocality. Apart from its clear relevance in situations where nonlocality is a resource, distillation protocols also play an important role in the understanding of information-theoretical principles for quantum theory. Here, we derive a necessary condition for nonlocality distillation from two copies and apply it, among other results, to show that one-dimensional (1D1\mathrm{D}1D) and 2D2\mathrm{D}2D quantum voids---faces of the nonlocal simplex set with no quantum realization---can be distilled up to PR boxes. With that, we generalize previous results in the literature, for instance, showing a broad class of postquantum correlations that make communication complexity trivial and violate the information causality principle.
Quantum theory admits correlations between distant parties that are stronger than those permitted by classical physics. Such correlations, which are termed nonlocal, have been studied extensively since their discovery by John Bell in 1964. This thesis makes progress on various aspects of quantum nonlocality both from a foundational and practical perspective. We begin by studying a foundational question on the relationship between nonlocality and quantum entanglement. We show that the strongest form of nonlocality, also called pseudo-telepathy or full nonlocality, can be demonstrated by non-maximally entangled states and prove that all pure entangled states can demonstrate full nonlocality in the many-copy scenario. We also provide non-trivial examples of fully nonlocal mixed states. We then turn to the study of another phenomenon in quantum theory which is essential in almost all demonstrations of non-classicality—measurement incompatibility. We generalise the notion of measurement incompatibility and show that our notion has strong operational relevance: it captures the randomness in the outcomes of an untrusted measurement device against a classical adversary. We use our formalism to derive new bounds on the experimental losses and noise that can be tolerated in quantum communication protocols before they become insecure. We then begin a systematic study of routed Bell experiments, a variant of standard Bell experiments that was introduced to demonstrate nonlocality over long distances in the presence of losses and noise. We formalize the notion of genuine long-range quantum correlations in routed Bell experiments and develop numerical and analytical tools to characterize them. We show that routed Bell experiments allow for the demonstration of long-range quantum correlations at arbitrarily large distances using only entangled qubit states. We then prove the security of fully device-independent (DI) quantum key distribution (QKD) protocols based on routed Bell tests and quantify the resulting improvement in key rate and distance compared to standard DI QKD protocols.
We first present a protocol for deterministically distilling nonlocality, building upon a recent result of Forster et al. [Phys. Rev. Lett. 102, 120401 (2009)10.1103/PhysRevLett.102.120401]. 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)10.1103/PhysRevLett.96.250401] 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.