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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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# I Peres-Horodecki criterion for a 3-qubit system

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