Exponentially many entanglement and correlation constraints for multipartite quantum states

TL;DR

This paper introduces an exponential family of correlation constraints for all finite-dimensional multipartite quantum states, derived via a generalized state inversion map, which generalize monogamy relations for pure states.

Contribution

It develops a systematic method to generate a vast set of entanglement constraints using a generalized state inversion map linked to shadow inequalities.

Findings

Provides exponential family of linear entropy inequalities for multipartite states

Derives monogamy relations for pure states' bipartite entanglement

Connects correlation constraints to shadow inequalities

Abstract

We present a family of correlations constraints that apply to all multipartite quantum systems of finite dimension. The size of this family is exponential in the number of subsystems. We obtain these relations by defining and investigating the generalized state inversion map. This map provides a systematic way to generate local unitary invariants of degree two in the state and is directly linked to the shadow inequalities proved by Rains [IEEE Trans. Inf. Theory 46, 54 (2000)]. The constraints are stated in terms of linear inequalities for the linear entropies of the subsystems. For pure quantum states they turn into monogamy relations that constrain the distribution of bipartite entanglement among the subsystems of the global state.