Second Law of Entanglement Manipulation with Entanglement Battery
arXiv:2405.10599 · doi:10.1103/kl56-p2vb
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 work, 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 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.
arXiv commentaccepted version in PRL; 6+10 pages, 2 figures; changes from v1: rewritten introduction, added appendix on batteries constrained with multiple measures
References in corpus (39)
- Quantum entanglement
- Concentrating Partial Entanglement by Local Operations
- Quantifying Entanglement
- Quantum Resource Theories
- Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
- Fundamental limitations for quantum and nano thermodynamics
- The second laws of quantum thermodynamics
- The Physics and Mathematics of the Second Law of Thermodynamics
- "Squashed Entanglement" - An Additive Entanglement Measure
- Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)
- Entanglement-assisted local manipulation of pure quantum states
- Continuity of quantum conditional information
- The Uniqueness Theorem for Entanglement Measures
- Entanglement Theory and the Second Law of Thermodynamics
- Embezzling Entangled Quantum States
- A Generalization of Quantum Stein's Lemma
- Are the laws of entanglement theory thermodynamical?
- Irreversibility in asymptotic manipulations of entanglement
- A reversible theory of entanglement and its relation to the second law
- Correlating thermal machines and the second law at the nanoscale
- Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof
- Quantum thermodynamics of correlated-catalytic state conversion at small-scale
- On asymptotic continuity of functions of quantum states
- Catalysis of entanglement and other quantum resources
- Relative entropy and squashed entanglement
- No second law of entanglement manipulation after all
- Correlation in Catalysts Enables Arbitrary Manipulation of Quantum Coherence
- On a gap in the proof of the generalised quantum Stein's lemma and its consequences for the reversibility of quantum resources
- Reversibility of quantum resources through probabilistic protocols
- Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation
- A solution of the generalised quantum Stein's lemma
- Catalysis in Action via Elementary Thermal Operations
- No-go theorem for entanglement distillation using catalysis
- Coherence manipulation in asymmetry and thermodynamics
- Catalysis always degrades external quantum correlations
- Catalytic and asymptotic equivalence for quantum entanglement
- Entanglement fluctuation theorems
- A hierarchy of thermal processes collapses under catalysis
- Gibbs-preserving operations requiring infinite amount of quantum coherence