Irreducible multi-particle correlations in states without maximal rank

TL;DR

This paper introduces a method to quantify irreducible multi-particle correlations in quantum states without maximal rank, revealing their distribution in stabilizer and GHZ states.

Contribution

It develops a continuity approach to calculate irreducible correlations in non-maximal rank states, providing explicit measures for stabilizer and GHZ states.

Findings

Quantified multi-particle correlations in stabilizer states

Analyzed correlation distribution in GHZ states

Overcame calculation difficulties for non-maximal rank states

Abstract

In a system of $n$ quantum particles, the correlations are classified into a series of irreducible $k$-particle correlations ($2\le k\le n$), where the irreducible $k$-particle correlation is the correlation appearing in the states of $k$ particles but not existing in the states of $k-1$ particles. A measure of the degree of irreducible $k$-particle correlation is defined based on the maximal entropy construction. By adopting a continuity approach, we overcome the difficulties in calculating the degrees of irreducible multi-particle correlations for the multi-particle states without maximal rank. In particular, we obtain the degrees of irreducible multi-particle correlations in the $n$-qubit stabilizer states and the $n$-qubit generalized GHZ states, which reveals the distribution of multi-particle correlations in these states.