Correlations and projective measurements in maximally entangled multipartite states

Multipartite quantum states constitute the key resource for quantum computation. The understanding of their internal structure is thus of great importance in the field of quantum information. This paper aims at examining the structure of multipartite maximally entangled pure states, using tools with a simple and intuitive physical meaning, namely, projective measurements and correlations. We first show how, in such states, a very simple relation arises between post-measurement expectation values and pre-measurement correlations. We then infer the consequences of this relation on the structure of the recently introduced entanglement metric, allowing us to provide an upper bound for the persistency of entanglement. The dependence of these features on the chosen measurement axis is underlined, and two simple optimization procedures are proposed, to find those maximizing the correlations. Finally, we apply our procedures onto some prototypical examples. •In maximally entangled states, correlators fully determine post-measurement averages.•Covariance matrices provide upper bounds for persistency and k-separability.•A procedure is proposed to optimize pair-wise correlations.•A procedure is proposed to find measurements breaking entanglement optimally.•Results are applied to cluster states and supersinglet states.