Local discrimination of mixed states

Abstract

We provide rigorous, efficiently computable and tight bounds on the average error probability of multiple-copy discrimination between qubit mixed states by Local Operations assisted with Classical Communication (LOCC). In contrast to the pure-state case, these experimentally feasible protocols perform strictly worse than the general collective ones. Our numerical results indicate that the gap between LOCC and collective error rates persists in the asymptotic limit. In order for LOCC and collective protocols to achieve the same accuracy, the former requires up to twice the number of copies of the latter. Our techniques can be used to bound the power of LOCC strategies in other similar settings, which is still one of the most elusive questions in quantum communication.

4 pages, 2 figures+ supplementary material

References in corpus (10)

• Quantum Cryptography
• The Quantum Chernoff Bound
• The Chernoff lower bound for symmetric quantum hypothesis testing
• Bounds on Multipartite Entangled Orthogonal State Discrimination Using Local Operations and Classical Communication
• The quantum Chernoff bound as a measure of distinguishability between density matrices: application to qubit and Gaussian states
• Discrimination of two channels by adaptive methods and its application to quantum system
• Multiple copy 2-state discrimination with individual measurements
• Minimum Decision Cost for Quantum Ensembles
• Secrecy content of two-qubit states
• Mixed state discrimination using optimal control

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