A note on the realignment criterion

Abstract

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.

11 pages, to appear in Journal of Physics A: Mathematical and Theoretical

References in corpus (3)

• Further results on the cross norm criterion for separability
• Bipartite quantum systems: on the realignment criterion and beyond
• On the relation between Schmidt coefficients and entanglement

Cited by in corpus (5)

• Entropic trade-off relations for quantum operations
• Entanglement detection in arbitrary dimensional bipartite quantum systems through partial realigned moments
• Characterizing generalized axisymmetric quantum states in $d\times d$ systems
• Physical realization of realignment criteria using structural physical approximation
• Correlation Minor Norms, Entanglement Detection and Discord