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

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