Separable Decompositions of Bipartite Mixed States

TL;DR

This paper introduces a practical scheme for decomposing bipartite mixed states into sums of product states by analyzing their correlation matrices and Bloch vectors, aiding in understanding quantum entanglement.

Contribution

The paper develops a new method leveraging correlation matrix decomposition and Bloch vector symmetries to achieve separable decompositions of bipartite mixed states.

Findings

The scheme effectively decomposes bipartite mixed states into separable forms.

The correlation matrix's symmetry constrains the local Bloch vectors.

Concrete examples demonstrate the method's applicability.

Abstract

We present a practical scheme for the decomposition of a bipartite mixed state into a sum of direct products of local density matrices, using the technique developed in Li and Qiao (Sci. Rep. 8: 1442, 2018). In the scheme, the correlation matrix which characterizes the bipartite entanglement is first decomposed into two matrices composed of the Bloch vectors of local states. Then we show that the symmetries of Bloch vectors are consistent with that of the correlation matrix, and the magnitudes of the local Bloch vectors are lower bounded by the correlation matrix. Concrete examples for the separable decompositions of bipartite mixed states are presented for illustration.