Reversibility of quantum resources through probabilistic protocols

Abstract

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 comment8+17 pages. v3: published version

References in corpus (33)

• Mixed State Entanglement and Quantum Error Correction
• Concentrating Partial Entanglement by Local Operations
• Quantum Resource Theories
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Distillation of secret key and entanglement from quantum states
• Robustness of entanglement
• The Physics and Mathematics of the Second Law of Thermodynamics
• Coding Theorem and Strong Converse for Quantum Channels
• Thermodynamics and the Measure of Entanglement
• Entanglement of pure states for a single copy
• The general structure of quantum resource theories
• The asymptotic entanglement cost of preparing a quantum state
• The entanglement cost under operations preserving the positivity of partial transpose
• Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints
• (Quantumness in the context of) Resource Theories
• Quantum Reverse Shannon Theorem
• Entanglement Theory and the Second Law of Thermodynamics
• The Quantum Reverse Shannon Theorem based on One-Shot Information Theory
• Strong Converse to the Quantum Channel Coding Theorem
• A Generalization of Quantum Stein's Lemma
• Are the laws of entanglement theory thermodynamical?
• Irreversibility in asymptotic manipulations of entanglement
• A strong converse for classical channel coding using entangled inputs
• A reversible theory of entanglement and its relation to the second law
• Benchmarking one-shot distillation in general quantum resource theories
• Strong converse rates for quantum communication
• Probabilistic transformations of quantum resources
• On a gap in the proof of the generalised quantum Stein's lemma and its consequences for the reversibility of quantum resources
• Irreversibility of Asymptotic Entanglement Manipulation Under Quantum Operations Completely Preserving Positivity of Partial Transpose
• "Pretty strong" converse for the quantum capacity of degradable channels
• One-Shot Yield-Cost Relations in General Quantum Resource Theories
• Distillable entanglement under dually non-entangling operations
• Overcoming entropic limitations on asymptotic state transformations through probabilistic protocols

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• Distillable entanglement under dually non-entangling operations
• No-go theorem for entanglement distillation using catalysis
• Thermodynamic Approach to Quantifying Incompatible Instruments
• Second Law of Entanglement Manipulation with Entanglement Battery
• Bipartite Bound Entanglement
• Entanglement cost for infinite-dimensional physical systems
• Asymptotic quantification of entanglement with a single copy
• Protocols for sharing genuine multipartite entanglement by employing copies of biseparable states
• The symplectic rank of non-Gaussian quantum states