Local hypothesis testing between a pure bipartite state and the white noise state

Abstract

In this paper, we treat a local discrimination problem in the framework of asymmetric hypothesis testing. We choose a known bipartite pure state $|\Psi ⟩$ as an alternative hypothesis, and the completely mixed state as a null hypothesis. As a result, we analytically derive an optimal type 2 error and an optimal POVM for one-way LOCC POVM and Separable POVM. For two-way LOCC POVM, we study a family of simple three-step LOCC protocols, and show that the best protocol in this family has strictly better performance than any one-way LOCC protocol in all the cases where there may exist difference between two-way LOCC POVM and one-way LOCC POVM.

18 pages, 4 figures

References in corpus (22)

• The Quantum Chernoff Bound
• A Generalization of Quantum Stein's Lemma
• Distinguishing Arbitrary Multipartite Basis Unambiguously Using Local Operations and Classical Communication
• Entanglement of multiparty stabilizer, symmetric, and antisymmetric states
• Distinguishability of Quantum States by Separable Operations
• State discrimination with error margin and its locality
• Error exponents in hypothesis testing for correlated states on a spin chain
• Optimal conclusive discrimination of two states can be achieved locally
• Discrimination with error margin between two states - Case of general occurrence probabilities -
• Group theoretical study of LOCC-detection of maximally entangled state using hypothesis testing
• Local distinguishability of orthogonal 2\otimes3 pure states
• Large deviations and Chernoff bound for certain correlated states on a spin chain
• Local Distinguishability of Orthogonal Quantum States and Generators of SU(N)
• Hypothesis testing for Gaussian states on bosonic lattices
• Typical support and Sanov large deviations of correlated states
• Quantum hypothesis testing with group symmetry
• Asymptotic distinguishability measures for shift-invariant quasi-free states of fermionic lattice systems
• Hypothesis testing for an entangled state produced by spontaneous parametric down conversion
• Construction of extremal local positive operator-valued measures under symmetry
• Locality and nonlocality in quantum pure-state identification problems
• Asymptotic local hypothesis testing between a pure bipartite state and the completely mixed state
• Testing for a pure state with local operations and classical communication

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• Discrimination of quantum states under locality constraints in the many-copy setting
• Locally-Measured Rényi Divergences