A note on the realignment criterion

Chi-Kwong Li, Yiu-Tung Poon, Nung-Sing Sze

Published 2011-03-13, updated 2011-07-04Version 2

For a quantum state in a bipartite system represented as a density matrix, researchers used the realignment matrix and functions on its singular values to study the separability of the quantum state. We obtain bounds for elementary symmetric functions of singular values of realignment matrices. This answers some open problems proposed by Lupo, Aniello, and Scardicchio. As a consequence, we show that the proposed scheme by these authors for testing separability would not work if the two subsystems of the bipartite system have the same dimension.