Peres-Horodecki criterion for a 3-qubit system

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SUMMARY

The Peres-Horodecki criterion is necessary and sufficient for determining entanglement in 2x2 and 2x3 density matrices but does not hold for 3-qubit systems represented by 8x8 matrices. Users should be cautious when applying this criterion to larger systems, as it may lead to incorrect conclusions about entanglement. The discussion references the original paper available at arxiv.org for further details.

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MMS
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Hello everyone,

Is the Peres-Horodecki criterion correct for any density matrix nxn?
I have a 3 qubit state (an 8x8 matrix) and I want to check whether it's entangled or not and I'm not sure if it's the right approach. Seems a little too cumbersome.

Thanks in advance.
 
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AFAIK the Peres criterion is sufficient for any density matrix, but it's if and only if only for 2 qubit density matrices, that is for your matrix it may fail and still you might have an entangled state
 

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