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Entanglement properties of multipartite informationally complete quantum measurements. (English) Zbl 1396.81019

Summary: We analyze tight informationally complete measurements for arbitrarily large multipartite systems and study their configurations of entanglement. We demonstrate that tight measurements cannot be exclusively composed neither of fully separable nor maximally entangled states. We establish an upper bound on the maximal number of fully separable states allowed by tight measurements and investigate the distinguished case in which every measurement operator carries the same amount of entanglement. Furthermore, we introduce the notion of nested tight measurements, i.e. multipartite tight informationally complete measurements such that every reduction to a certain number of parties induces a lower dimensional tight measurement, proving that they exist for any number of parties and internal levels.

MSC:

81P15 Quantum measurement theory, state operations, state preparations
81P40 Quantum coherence, entanglement, quantum correlations
46G10 Vector-valued measures and integration
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