Remarks on entanglement measures and non-local state distinguishability

Abstract

We investigate the properties of three entanglement measures that quantify the statistical distinguishability of a given state with the closest disentangled state that has the same reductions as the primary state. In particular, we concentrate on the relative entropy of entanglement with reversed entries. We show that this quantity is an entanglement monotone which is strongly additive, thereby demonstrating that monotonicity under local quantum operations and strong additivity are compatible in principle. In accordance with the presented statistical interpretation which is provided, this entanglement monotone, however, has the property that it diverges on pure states, with the consequence that it cannot distinguish the degree of entanglement of different pure states. We also prove that the relative entropy of entanglement with respect to the set of disentangled states that have identical reductions to the primary state is an entanglement monotone. We finally investigate the trace-norm measure and demonstrate that it is also a proper entanglement monotone.

7 pages, 1 figure

References in corpus (27)

• Mixed State Entanglement and Quantum Error Correction
• A computable measure of entanglement
• Quantifying Entanglement
• Entanglement Measures and Purification Procedures
• On the volume of the set of mixed entangled states
• Entanglement monotones
• Entanglement Measures under Symmetry
• The asymptotic entanglement cost of preparing a quantum state
• Limits for entanglement measures
• An improved bound on distillable entanglement
• A comparison of entanglement measures
• Entanglement in Quantum Information Theory
• Implementing the quantum random walk
• The entanglement cost under operations preserving the positivity of partial transpose
• Statistical Inference, Distinguishability of Quantum States, And Quantum Entanglement
• A rigorous treatment of distillable entanglement
• The Uniqueness Theorem for Entanglement Measures
• Entanglement measures and the Hilbert-Schmidt distance
• Entanglement cost of mixed states
• On the quantification of entanglement in infinite-dimensional quantum systems
• A new entanglement measure induced by the Hilbert-Schmidt norm
• The asymptotic relative entropy of entanglement
• Bounds on relative entropy of entanglement for multi-party systems
• On the geometry of entangled states
• Operator monotones, the reduction criterion and the relative entropy
• Classical information and distillable entanglement
• The reduction of the closest disentangled states

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