Nonadditivity of Rains' bound for distillable entanglement

Abstract

Rains' bound is arguably the best known upper bound of the distillable entanglement by operations completely preserving positivity of partial transpose (PPT) and was conjectured to be additive and coincide with the asymptotic relative entropy of entanglement. We disprove both conjectures by explicitly constructing a special class of mixed two-qubit states. We then introduce an additive semidefinite programming lower bound ($E_M$) for the asymptotic Rains' bound, and it immediately becomes a computable lower bound for entanglement cost of bipartite states. Furthermore, $E_M$ is also proved to be the best known upper bound of the PPT-assisted deterministic distillable entanglement and gives the asymptotic rates for all pure states and some class of genuinely mixed states.

6 pages, title changed, closed to the published version

References in corpus (6)

• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• Closed formula for the relative entropy of entanglement
• Closed formula for the relative entropy of entanglement in all dimensions
• Pure-state transformations and catalysis under operations that completely preserve positivity of partial transpose
• Indistinguishability of bipartite states by positive-partial-transpose operations in the many-copy scenario
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• Non-asymptotic entanglement distillation
• Adaptive recurrence quantum entanglement distillation for two-Kraus-operator channels
• Practical distributed quantum information processing with LOCCNet
• Irreversibility of Asymptotic Entanglement Manipulation Under Quantum Operations Completely Preserving Positivity of Partial Transpose
• One-shot entanglement distillation beyond local operations and classical communication
• Multipartite entanglement measures: a review
• Exponential clustering of bipartite quantum entanglement at arbitrary temperatures
• Pursuing the fundamental limits for quantum communication
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme
• Interplay of entanglement structures and stabilizer entropy in spin models
• Censorship of Quantum Resources in Quantum Networks
• Quantifying the unextendibility of entanglement
• Quantifying magic via quantum $(\alpha ,\beta )$ Jensen-Shannon divergence
• Tripartite-to-bipartite Entanglement Transformation by Stochastic Local Operations and Classical Communication and the Structure of Matrix Spaces
• Dynamic LOCC Circuits for Automated Entanglement Manipulation