I Peres-Horodecki criterion for a 3-qubit system

[MMS]

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.

 

[nashed]

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

 

[Zarqon]

The Peres-Horodecki criterion is necessary and sufficient only for 2x2 and 2x3 systems, see e.g. the arxiv version of their paper: https://arxiv.org/pdf/quant-ph/9605038.pdf