Distribution of entanglement and correlations in all finite dimensions

TL;DR

This paper derives a fundamental equality relating correlations in multipartite finite-dimensional quantum systems, providing a necessary condition for the compatibility of local and global states, with implications for entanglement monogamy and conservation laws.

Contribution

It introduces a universal correlation equality for finite-dimensional quantum systems, establishing a new monogamy relation for entanglement and constraints on marginal and joint states.

Findings

Derives a correlation equality for multipartite quantum states.

Establishes a necessary condition for marginal and global state compatibility.

Reveals a general monogamy relation for entanglement.

Abstract

The physics of a many-particle system is determined by the correlations in its quantum state. Therefore, analyzing these correlations is the foremost task of many-body physics. Any 'a priori' constraint for the properties of the global vs. the local states---the so-called marginals---would help in order to narrow down the wealth of possible solutions for a given many-body problem, however, little is known about such constraints. We derive an equality for correlation-related quantities of any multipartite quantum system composed of finite-dimensional local parties. This relation defines a necessary condition for the compatibility of the marginal properties with those of the joint state. While the equality holds both for pure and mixed states, the pure-state version containing only entanglement measures represents a fully general monogamy relation for entanglement. These findings have interesting implications in terms of conservation laws for correlations, and also with respect to topology.