Correlation and Entanglement of Multipartite States

TL;DR

This paper develops a classification and measure for classical and quantum correlations in multipartite quantum systems using SU(n) representations, comparing with entanglement measures and analyzing particle symmetry effects.

Contribution

It introduces a new correlation measure based on SU(n) representations and characterizes entanglement using singular values and invariant parameters, extending to multipartite and identical particle systems.

Findings

Correlation measure based on nonzero singular values of the correlation matrix.

Explicit bipartite entanglement condition for qubits using invariant parameters.

Analysis of exchange symmetry effects on correlations in identical particle systems.

Abstract

We derive a classification and a measure of classical- and quantum-correlation of multipartite qubit, qutrit, and in general, $n$-level systems, in terms of SU$(n)$ representations of density matrices. We compare the measure for the case of bipartite correlation with concurrence and the entropy of entanglement. The characterization of correlation is in terms of the number of nonzero singular values of the correlation matrix, but that of mixed state entanglement requires additional invariant parameters in the density matrix. For the bipartite qubit case, the condition for mixed state entanglement is written explicitly in terms of the invariant paramters in the density matrix. For identical particle systems we analyze the effects of exchange symmetry on classical and quantum correlation.