Irreducible MultiQutrit Correlations in Greenberger-Horne-Zeilinger Type States

TL;DR

This paper investigates the degrees of irreducible multi-party correlations in specific n-qutrit GHZ-type states, revealing differences from qubit states and characterizing correlation distributions in maximal slice states.

Contribution

It extends the continuity approach to analyze multi-party correlations in high-dimensional systems, providing new insights into the structure of n-qutrit GHZ-type states.

Findings

Irreducible 2-party and n-party correlations are nonzero in certain pure states.

Maximal slice states have no irreducible n-qutrit correlation.

Correlation distributions are determined by (n-1)-qutrit reduced states.

Abstract

Following the idea of the continuity approach in [D. L. Zhou, Phys. Rev. Lett. 101, 180505 (2008)], we obtain the degrees of irreducible multi-party correlations in two families of $n$-qutrit Greenberger-Horne-Zeilinger type states. For the pure states in one of the families, the irreducible 2-party, $n$-party and $(n-m)$-party ($0< m < n-2$) correlations are nonzero, which is different from the $n$-qubit case. We also derive the correlation distributions in the $n$-qutrit maximal slice state, which can be uniquely determined by its $(n-1)$-qutrit reduced density matrices among pure states. It is proved that there is no irreducible $n$-qutrit correlation in the maximal slice state. This enlightens us to give a discussion about how to characterize the pure states with irreducible $n$-party correlation in arbitrarily high-dimensional systems by the way of the continuity approach.