Further results on entanglement detection and quantification from the correlation matrix criterion

TL;DR

This paper explores the correlation matrix criterion's effectiveness in detecting and quantifying entanglement in bipartite quantum states, demonstrating its superiority over other criteria in certain cases and its use in measuring entanglement.

Contribution

It provides examples where the correlation matrix criterion detects entanglement missed by PPT and CCNR criteria, and shows how it can quantify entanglement in pure and mixed states.

Findings

CM can detect entanglement missed by PPT and CCNR.

CM can measure entanglement of pure states.

Lower bounds for tangle are obtained using CM.

Abstract

The correlation matrix (CM) criterion is a recently derived powerful sufficient condition for the presence of entanglement in bipartite quantum states of arbitrary dimensions. It has been shown that it can be stronger than the positive partial transpose (PPT) criterion, as well as the computable cross norm or realignment (CCNR) criterion in different situations. However, it remained as an open question whether there existed sets of states for which the CM criterion could be stronger than both criteria simultaneously. Here, we give an affirmative answer to this question by providing examples of entangled states that scape detection by both the PPT and CCNR criteria whose entanglement is revealed by the CM condition. We also show that the CM can be used to measure the entanglement of pure states and obtain lower bounds for the entanglement measure known as tangle for general (mixed) states.