Informationally complete quantum measurements & entanglement bounds

Michel R. P. Planat

Knots, links and (informationally complete) quantum measurements

Tao Li, Le-Min Lai, Deng-Feng Liang +2 more

Jakub Czartowski, Dardo Goyeneche, Karol Życzkowski

Abstract 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.

Le-Min Lai, Tao Li, Shao-Ming Fei +1 more

Rui‐Zhou Liang, Zhi‐Xiang Jin, Wei Chen +1 more

Abstract In this work, the framework of ‐nonseparability is utilized to investigate parameterized multipartite entanglement measures. A ‐nonseparable revised informationally complete entanglement measure(‐RICEM) is proposed for ‐partite quantum systems(), capable of identifying all ‐nonseparable states across arbitrary ‐partite configurations. The ‐RICEM offers enhanced resolution in entanglement characterization compared to conventional measures. It is proven that the proposed ‐nonseparable measure is a valid entanglement measure, satisfying entanglement monotonicity, convexity, and nonzero for ‐nonseparable states. Using properties of ‐concurrence under partial transposition and realignment, analytical lower bounds for mixed states in ‐RICEM are derived. Furthermore, operational connections between ‐RICEM and the global negativity measure are established. A comparative analysis between the genuine multipartite entanglement GME‐RICEM and existing genuine multipartite entanglement measures reveals distinct advantages in state discrimination capability.

Jakub Czartowski, Dardo Goyeneche, Karol Życzkowski

We present a comprehensible introduction to tight informationally complete measurements for arbitrarily large multipartite systems and study their allowed entanglement configurations, focusing on those requiring simplest possible quantum resources. We demonstrate that tight measurements cannot be exclusively composed neither by fully separable nor maximally entangled states, according to a selected measure of entanglement. We establish an upper bound on the maximal number of fully separable states allowed by tight measurements and we study the distinguished case in which every measurement operator has 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.