Entanglement properties of multipartite informationally complete quantum measurements

TL;DR

This paper investigates the entanglement characteristics of tight informationally complete measurements in multipartite quantum systems, revealing their limitations and introducing the concept of nested tight measurements with broad applicability.

Contribution

It provides new bounds on entanglement in tight measurements and introduces nested tight measurements, expanding understanding of quantum measurement configurations.

Findings

Tight measurements cannot be solely composed of fully separable or maximally entangled states.

An upper bound on the number of fully separable states in tight measurements is established.

Nested tight measurements exist for any number of parties and internal levels.

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.