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:2405.10599 · Physical Review Letters

Second Law of Entanglement Manipulation with an Entanglement Battery

Ray Ganardi, Tulja Varun Kondra, Nelly H. Y. Ng, Alexander Streltsov

Published May 19, 2025• 8 citations
arXivHTMLPDF

Abstract

A central question since the beginning of quantum information science is how two distant parties can convert one entangled state into another. It has been conjectured that such conversions could be executed reversibly in an asymptotic regime, mirroring the reversible nature of Carnot cycles in classical thermodynamics. While a conclusive proof of this conjecture has been missing so far, earlier studies have excluded reversible entanglement manipulation in various settings. In this Letter, we show that arbitrary mixed state entanglement transformations can be made reversible under local operations and classical communication, when assisted by an entanglement battery-an auxiliary quantum system that stores and supplies entanglement in a way that ensures no net entanglement is lost. In particular, the rate of transformation in the asymptotic limit can be quantitatively expressed as a ratio of entanglement present within the quantum states involved. Our setting allows us to consider different entanglement quantifiers which give rise to unique principles governing state transformations, effectively constituting diverse manifestations of a "second law" of entanglement manipulation. These findings resolve a long-standing open question on the reversible manipulation of entangled states and are also applicable to multipartite entanglement and other quantum resource theories, including quantum thermodynamics.

DOI
10.1103/kl56-p2vb

Related papers

No second law of entanglement manipulation after all

Ludovico Lami, Bartosz Regula

Abstract Many fruitful analogies have emerged between the theories of quantum entanglement and thermodynamics, motivating the pursuit of an axiomatic description of entanglement akin to the laws of thermodynamics. A long-standing open problem has been to establish a true second law of entanglement, and in particular a unique function that governs all transformations between entangled systems, mirroring the role of entropy in thermodynamics. Contrary to previous promising evidence, here we show that this is impossible and that no direct counterpart to the second law of thermodynamics can be established. This is accomplished by demonstrating the irreversibility of entanglement theory from first principles. Assuming only the most general microscopic physical constraints of entanglement manipulation, we show that entanglement theory is irreversible under all non-entangling transformations. We furthermore rule out reversibility without significant entanglement expenditure, showing that reversible entanglement transformations require the generation of macroscopically large amounts of entanglement according to certain measures. Our results not only reveal fundamental differences between quantum entanglement transformations and thermodynamic processes, but also showcase a unique property of entanglement that distinguishes it from other known quantum resources.

arXiv:2111.02438•Nature Physics•Jan 23, 2023•45 citations

A reversible theory of entanglement and its relation to the second law

Brandão, FGSL, Martin Bodo Plenio

We consider the manipulation of multipartite entangled states in the limit of many copies under quantum operations that asymptotically cannot generate entanglement. In stark contrast to the manipulation of entanglement under local operations and classical communication, the entanglement shared by two or more parties can be reversibly interconverted in this setting. The unique entanglement measure is identified as the regularized relative entropy of entanglement, which is shown to be equal to a regularized and smoothed version of the logarithmic robustness of entanglement. Here we give a rigorous proof of this result, which is fundamentally based on a certain recent extension of quantum Stein's Lemma, giving the best measurement strategy for discriminating several copies of an entangled state from an arbitrary sequence of non-entangled states, with an optimal distinguishability rate equal to the regularized relative entropy of entanglement. We moreover analyse the connection of our approach to axiomatic formulations of the second law of thermodynamics. © Springer-Verlag 2010.

•Mar 1, 2010•35 citations

Reversibility of quantum resources through probabilistic protocols

Bartosz Regula, Ludovico Lami

Among the most fundamental questions in the manipulation of quantum resources such as entanglement is the possibility of reversibly transforming all resource states. The key consequence of this would be the identification of a unique entropic resource measure that exactly quantifies the limits of achievable transformation rates. Remarkably, previous results claimed that such asymptotic reversibility holds true in very general settings; however, recently those findings have been found to be incomplete, casting doubt on the conjecture. Here we show that it is indeed possible to reversibly interconvert all states in general quantum resource theories, as long as one allows protocols that may only succeed probabilistically. Although such transformations have some chance of failure, we show that their success probability can be ensured to be bounded away from zero, even in the asymptotic limit of infinitely many manipulated copies. As in previously conjectured approaches, the achievability here is realised through operations that are asymptotically resource non-generating, and we show that this choice is optimal: smaller sets of transformations cannot lead to reversibility. Our methods are based on connecting the transformation rates under probabilistic protocols with strong converse rates for deterministic transformations, which we strengthen into an exact equivalence in the case of entanglement distillation.

arXiv:2309.07206•Nature Communications•Apr 17, 2024•18 citations

Efficient Entanglement Manipulation Cookbook: From Mixing to a Computational Second Law

Ilia Ryzov, Faedi Loulidi, David Elkouss

Quantum entanglement is an essential resource for implementing practical quantum devices. However, for the resource to be useful in large-scale applications, it must be accessible to parties with limited computational resources. Computational entanglement measures quantify the usefulness of entanglement in the presence of limited computational resources in the practical setting of non-asymptotic manipulations. In this paper, we build a framework of non-asymptotic efficient entanglement manipulations by systematically analyzing a wide range of properties of two recently introduced computational entanglement measures: the computational one-shot distillable entanglement and cost. To do so, we adapt definitions of some common properties of scalar entanglement measures to the case in which only lower or upper function bounds are available. Using the developed framework, we then proceed to investigate the mathematical behavior of the newly introduced entanglement measures under probabilistic state mixing and tensor-product operations. Furthermore, we analyze how the values of both measures change under local unitary and LOCC transformations. For this, we derive an explicit quantitative connection between the geometry of projective-net-generated families of states and their computational one-shot distillable entanglement, and use this connection to establish an unconditional separation between computational and information-theoretic one-shot distillable entanglement. Furthermore, we investigate the robustness of efficiently accessible entanglement against noise and derive the first quantitative continuity bound on computational distillable entanglement. Finally, as an application of the developed "dictionary" of properties, we establish a fundamental relation between computational entanglement measures that we call the "Second Law of Efficient Entanglement Manipulation".

arXiv:2509.21988•Sep 26, 2025•0 citations

Entanglement manipulation under non-entangling operations

Fernando G. S. L. Brandão, Martin Bodo Plenio

We demonstrate that entanglement shared by two or more parties can be asymptotically reversibly interconverted when one considers the set of operations which asymptotically cannot generate entanglement. In this scenario we find that the entanglement of every quantum state is uniquely characterized by a single quantity: the regularized relative entropy of entanglement. The main technical tool is a generalization of quantum Stein's Lemma, which gives optimal discrimination rates in quantum hypothesis testing, to the case in which the alternative hypothesis might vary over sets of correlated states. We analyze the connection of our approach to recent rigorous formulations of the second law of thermodynamics.

Journal of Physics Conference Series•Jan 7, 2009•1 citation

Entanglement fluctuation theorems

Alvaro Martin Alhambra, Lluís Masanes, Jonathan Oppenheim +1 more

Pure-state entanglement transformations have been thought of as irreversible, with reversible transformations generally only possible in the limit of many copies. Here, we show that reversible entanglement transformations do not require processing on the many-copy level but can instead be undertaken on individual systems, provided the amount of entanglement which is produced or consumed is allowed to fluctuate. We derive necessary and sufficient conditions for entanglement manipulations in this case. As a corollary, we derive an equation which quantifies the fluctuations of entanglement, which is formally identical to the Jarzynski fluctuation equality found in thermodynamics. One can also relate a forward entanglement transformation to its reverse process in terms of the entanglement cost of such a transformation, in a manner equivalent to the Crooks relation. We show that a strong converse theorem for entanglement transformations is formally related to the second law of thermodynamics, while the fact that the Schmidt rank of an entangled state cannot increase is related to the third law of thermodynamics. Achievability of the protocols is done by introducing an entanglement battery, a device which stores entanglement and uses an amount of entanglement that is allowed to fluctuate but with an average cost which is still optimal. This allows us to also solve the problem of partial entanglement recovery, and in fact, we show that entanglement is fully recovered. Allowing the amount of consumed entanglement to fluctuate also leads to improved and optimal entanglement dilution protocols.

arXiv:1709.06139•Physical Review A•Jul 15, 2019•8 citations
A central question since the beginning of quantum information science is how two distant parties can convert one entangled state into another. It has been conjectured that such conversions could be executed reversibly in an asymptotic regime, mirroring the reversible nature of Carnot cycles in classical thermodynamics. While a conclusive proof of this conjecture has been missing so far, earlier studies have excluded reversible entanglement manipulation in various settings. In this Letter, we show that arbitrary mixed state entanglement transformations can be made reversible under local operations and classical communication, when assisted by an entanglement battery-an auxiliary quantum system that stores and supplies entanglement in a way that ensures no net entanglement is lost. In particular, the rate of transformation in the asymptotic limit can be quantitatively expressed as a ratio of entanglement present within the quantum states involved. Our setting allows us to consider different entanglement quantifiers which give rise to unique principles governing state transformations, effectively constituting diverse manifestations of a "second law" of entanglement manipulation. These findings resolve a long-standing open question on the reversible manipulation of entangled states and are also applicable to multipartite entanglement and other quantum resource theories, including quantum thermodynamics.
Abstract Many fruitful analogies have emerged between the theories of quantum entanglement and thermodynamics, motivating the pursuit of an axiomatic description of entanglement akin to the laws of thermodynamics. A long-standing open problem has been to establish a true second law of entanglement, and in particular a unique function that governs all transformations between entangled systems, mirroring the role of entropy in thermodynamics. Contrary to previous promising evidence, here we show that this is impossible and that no direct counterpart to the second law of thermodynamics can be established. This is accomplished by demonstrating the irreversibility of entanglement theory from first principles. Assuming only the most general microscopic physical constraints of entanglement manipulation, we show that entanglement theory is irreversible under all non-entangling transformations. We furthermore rule out reversibility without significant entanglement expenditure, showing that reversible entanglement transformations require the generation of macroscopically large amounts of entanglement according to certain measures. Our results not only reveal fundamental differences between quantum entanglement transformations and thermodynamic processes, but also showcase a unique property of entanglement that distinguishes it from other known quantum resources.
We consider the manipulation of multipartite entangled states in the limit of many copies under quantum operations that asymptotically cannot generate entanglement. In stark contrast to the manipulation of entanglement under local operations and classical communication, the entanglement shared by two or more parties can be reversibly interconverted in this setting. The unique entanglement measure is identified as the regularized relative entropy of entanglement, which is shown to be equal to a regularized and smoothed version of the logarithmic robustness of entanglement. Here we give a rigorous proof of this result, which is fundamentally based on a certain recent extension of quantum Stein's Lemma, giving the best measurement strategy for discriminating several copies of an entangled state from an arbitrary sequence of non-entangled states, with an optimal distinguishability rate equal to the regularized relative entropy of entanglement. We moreover analyse the connection of our approach to axiomatic formulations of the second law of thermodynamics. © Springer-Verlag 2010.
Among the most fundamental questions in the manipulation of quantum resources such as entanglement is the possibility of reversibly transforming all resource states. The key consequence of this would be the identification of a unique entropic resource measure that exactly quantifies the limits of achievable transformation rates. Remarkably, previous results claimed that such asymptotic reversibility holds true in very general settings; however, recently those findings have been found to be incomplete, casting doubt on the conjecture. Here we show that it is indeed possible to reversibly interconvert all states in general quantum resource theories, as long as one allows protocols that may only succeed probabilistically. Although such transformations have some chance of failure, we show that their success probability can be ensured to be bounded away from zero, even in the asymptotic limit of infinitely many manipulated copies. As in previously conjectured approaches, the achievability here is realised through operations that are asymptotically resource non-generating, and we show that this choice is optimal: smaller sets of transformations cannot lead to reversibility. Our methods are based on connecting the transformation rates under probabilistic protocols with strong converse rates for deterministic transformations, which we strengthen into an exact equivalence in the case of entanglement distillation.
Quantum entanglement is an essential resource for implementing practical quantum devices. However, for the resource to be useful in large-scale applications, it must be accessible to parties with limited computational resources. Computational entanglement measures quantify the usefulness of entanglement in the presence of limited computational resources in the practical setting of non-asymptotic manipulations. In this paper, we build a framework of non-asymptotic efficient entanglement manipulations by systematically analyzing a wide range of properties of two recently introduced computational entanglement measures: the computational one-shot distillable entanglement and cost. To do so, we adapt definitions of some common properties of scalar entanglement measures to the case in which only lower or upper function bounds are available. Using the developed framework, we then proceed to investigate the mathematical behavior of the newly introduced entanglement measures under probabilistic state mixing and tensor-product operations. Furthermore, we analyze how the values of both measures change under local unitary and LOCC transformations. For this, we derive an explicit quantitative connection between the geometry of projective-net-generated families of states and their computational one-shot distillable entanglement, and use this connection to establish an unconditional separation between computational and information-theoretic one-shot distillable entanglement. Furthermore, we investigate the robustness of efficiently accessible entanglement against noise and derive the first quantitative continuity bound on computational distillable entanglement. Finally, as an application of the developed "dictionary" of properties, we establish a fundamental relation between computational entanglement measures that we call the "Second Law of Efficient Entanglement Manipulation".
We demonstrate that entanglement shared by two or more parties can be asymptotically reversibly interconverted when one considers the set of operations which asymptotically cannot generate entanglement. In this scenario we find that the entanglement of every quantum state is uniquely characterized by a single quantity: the regularized relative entropy of entanglement. The main technical tool is a generalization of quantum Stein's Lemma, which gives optimal discrimination rates in quantum hypothesis testing, to the case in which the alternative hypothesis might vary over sets of correlated states. We analyze the connection of our approach to recent rigorous formulations of the second law of thermodynamics.
Pure-state entanglement transformations have been thought of as irreversible, with reversible transformations generally only possible in the limit of many copies. Here, we show that reversible entanglement transformations do not require processing on the many-copy level but can instead be undertaken on individual systems, provided the amount of entanglement which is produced or consumed is allowed to fluctuate. We derive necessary and sufficient conditions for entanglement manipulations in this case. As a corollary, we derive an equation which quantifies the fluctuations of entanglement, which is formally identical to the Jarzynski fluctuation equality found in thermodynamics. One can also relate a forward entanglement transformation to its reverse process in terms of the entanglement cost of such a transformation, in a manner equivalent to the Crooks relation. We show that a strong converse theorem for entanglement transformations is formally related to the second law of thermodynamics, while the fact that the Schmidt rank of an entangled state cannot increase is related to the third law of thermodynamics. Achievability of the protocols is done by introducing an entanglement battery, a device which stores entanglement and uses an amount of entanglement that is allowed to fluctuate but with an average cost which is still optimal. This allows us to also solve the problem of partial entanglement recovery, and in fact, we show that entanglement is fully recovered. Allowing the amount of consumed entanglement to fluctuate also leads to improved and optimal entanglement dilution protocols.