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A criterion for testing multi-particle NPT entanglement

B. Zeng·D. L. Zhou·P. Zhang·Z. Xu·L. You
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Abstract

We revisit the criterion of multi-particle entanglement based on the overlaps of a given quantum state $ρ$ with maximally entangled states. For a system of $m$ particles, each with $N$ distinct states, we prove that $ρ$ is $m$-particle negative partial transpose (NPT) entangled, if there exists a maximally entangled state $|{\rm MES}>$, such that $<{\rm MES}|ρ|{\rm MES}>>{1}/{N}$. While this sufficiency condition is weaker than the Peres-Horodecki criterion in all cases, it applies to multi-particle systems, and becomes especially useful when the number of particles ($m$) is large. We also consider the converse of this criterion and illustrate its invalidity with counter examples.

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B. Zeng, D. L. Zhou, P. Zhang, Z. Xu, L. You. 2003-05-16. A criterion for testing multi-particle NPT entanglement. https://arxiv.org/abs/quant-ph/0305091

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