A study of LOCC-detection of a maximally entangled state using hypothesis testing

Abstract

We study how well answer to the question ``Is the given quantum state equal to a certain maximally entangled state?'' using LOCC, in the context of hypothesis testing. Under several locality and invariance conditions, optimal tests will be derived for several special cases by using basic theory of group representations. Some optimal tests are realized by performing quantum teleportation and checking whether the state is teleported. We will also give a finite process for realizing some optimal tests. The performance of the tests will be numerically compared.

References in corpus (11)

• Separability of Mixed States: Necessary and Sufficient Conditions
• Bell Inequalities and the Separability Criterion
• Optimization of entanglement witnesses
• Detection of entanglement with few local measurements
• A rigorous treatment of distillable entanglement
• Experimental Detection of Entanglement with Polarized Photons
• Bounds on Multipartite Entangled Orthogonal State Discrimination Using Local Operations and Classical Communication
• Optimal sequence of quantum measurements in the sense of Stein's lemma in quantum hypothesis testing
• Local copying and local discrimination as a study for non-locality of a set
• Construction of extremal local positive operator-valued measures under symmetry
• Local observables for entanglement witnesses

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