On a gap in the proof of the generalised quantum Stein's lemma and its consequences for the reversibility of quantum resources

Abstract

We show that the proof of the generalised quantum Stein's lemma [Brandão & Plenio, Commun. Math. Phys. 295, 791 (2010)] is not correct due to a gap in the argument leading to Lemma III.9. Hence, the main achievability result of Brandão & Plenio is not known to hold. This puts into question a number of established results in the literature, in particular the reversibility of quantum entanglement [Brandão & Plenio, Commun. Math. Phys. 295, 829 (2010); Nat. Phys. 4, 873 (2008)] and of general quantum resources [Brandão & Gour, Phys. Rev. Lett. 115, 070503 (2015)] under asymptotically resource non-generating operations. We discuss potential ways to recover variants of the newly unsettled results using other approaches.

29 pages; in v2 we added Section V.D and Section VI, and corrected several small typos; v5 contains minor corrections in the discussion in Section V

References in corpus (4)

• Distillation of secret key and entanglement from quantum states
• Measuring the quality of a quantum reference frame: the relative entropy of frameness
• Entanglement Theory and the Second Law of Thermodynamics
• No second law of entanglement manipulation after all

Cited by in corpus (22)

• Catalysis of entanglement and other quantum resources
• No second law of entanglement manipulation after all
• Tight constraints on probabilistic convertibility of quantum states
• Testing the quantum nature of gravity without entanglement
• Reversibility of quantum resources through probabilistic protocols
• Every quantum helps: Operational advantage of quantum resources beyond convexity
• A solution of the generalised quantum Stein's lemma
• Distillable entanglement under dually non-entangling operations
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme
• Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories
• No-go theorem for entanglement distillation using catalysis
• Maximally entangled mixed states for a fixed spectrum do not always exist
• Parallelization of Adaptive Quantum Channel Discrimination in the Non-Asymptotic Regime
• Entanglement monogamy via multivariate trace inequalities
• Continuity of entropies via integral representations
• Second Law of Entanglement Manipulation with Entanglement Battery
• Black Box Work Extraction and Composite Hypothesis Testing
• Asymptotic quantification of entanglement with a single copy
• Multipartite entanglement theory with entanglement-nonincreasing operations
• Universal tester for multiple independence testing and classical-quantum arbitrarily varying multiple access channel
• Nonexistence of maximally entangled mixed states for a fixed spectrum
• Quantum geometric tensor determines the pure-state i.i.d. conversion rate in the resource theory of asymmetry for any compact Lie group