Conditions for monogamy of quantum correlations in multipartite systems

TL;DR

This paper explores the conditions under which quantum correlations exhibit monogamy in multipartite systems, providing mathematical proofs that relate the monogamous nature of measures to their powers and state types.

Contribution

It establishes new theoretical conditions linking the monogamy of quantum correlation measures to their powers and state purity, advancing understanding in quantum information theory.

Findings

Monogamous measures remain monogamous when their power is increased.

Non-monogamous measures remain non-monogamous when their power is decreased.

Monogamy of convex measures for pure states implies monogamy for mixed states.

Abstract

Monogamy of quantum correlations is a vibrant area of research because of its potential applications in several areas in quantum information ranging from quantum cryptography to co-operative phenomena in many-body physics. In this paper, we investigate conditions under which monogamy is preserved for functions of quantum correlation measures. We prove that a monogamous measure remains monogamous on raising its power, and a non-monogamous measure remains non-monogamous on lowering its power. We also prove that monogamy of a convex quantum correlation measure for arbitrary multipartite pure quantum state leads to its monogamy for mixed states in the same Hilbert space. Monogamy of squared negativity for mixed states and that of entanglement of formation follow as corollaries of our results.