A note on generalized concurrences and entanglement detection

TL;DR

This paper investigates the effectiveness of generalized concurrences in detecting entanglement in bipartite quantum states, revealing limitations in their ability to identify all entangled states.

Contribution

The study demonstrates that generalized concurrences are not always sufficient for entanglement detection, especially for certain 2 x 4 states of rank 2, and identifies undetected entangled states.

Findings

Generalized concurrences do not provide necessary and sufficient conditions for separability.

Some entangled states remain undetected by generalized concurrences.

Limitations of generalized concurrences in specific bipartite quantum systems.

Abstract

We study generalized concurrences as a tool to detect the entanglement of bipartite quantum systems. By considering the case of 2 X 4 states of rank 2, we prove that generalized concurrences do not, in general, give a necessary and sufficient condition of separability. We identify a set of entangled states which are undetected by this method.