Talk:Peres–Horodecki criterion

What is T(ρ)?

--XAliothx (talk) 11:23, 26 July 2010 (UTC)

Is the transposition map applied to the operator ρ. In matrix language, T(ρ) = ρ^T. But note that in the article the map is $I\otimes T$, not just T. Tercer (talk) 03:39, 27 July 2010 (UTC)

Issues

There are a few problems with the "Demonstration" section:

The "demonstration" is really a proof, or what is claiming to be a proof. The Peres-Horodecki criterion is a theorem that gives a characterization of separability in the 2 by 2 and 2 by 3 case.

The content of that section is confused, if not outright incoherent, I am sorry to say. The issue at hand is simple. Given a state ρ that satisfies PPT, show that it's separable. We have two facts:

• Fact 1. If ρ is not separable, then there exists an "entanglement witness", i.e. a positive map Φ such that (id⊗Φ)(ρ) is not positive. This was due to the Horodecki's and invokes the Hanh-Banach theorem.

• Fact 2. Woronowicz's theorem for positive maps on low dimensional matrix algebras.

So if ρ is not separable in the low dimensional case, ρ cannot be PPT for this would contradict fact 1. So Woronowicz's theorem is integral to the proof, not a corollary, as that section right now seems to imply. Mct mht (talk) 05:50, 16 March 2011 (UTC)

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In the "example" section it is never written what state |psi^-> actually is. — Preceding unsigned comment added by 147.188.42.176 (talk) 10:22, 24 August 2016 (UTC)