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Although there is no standard measure of entanglement, the GHZ states

$|GHZ\rangle=\frac{1}{\sqrt{2}}(|0\rangle^{\otimes n}+|1\rangle^{\otimes n})$

are often deemed as maximally entangled states of $n$ qubits. We know by now that even separable states can exhibit correlations that are impossible in the classical world. This makes me wonder: is there a similar characterization of separable states that exhibit maximum non-classical correlations?

For example, I imagine that states of the form

$\rho=(1/4)(|0\rangle\langle 0|\otimes|+\rangle\langle +|)+(|1\rangle\langle 1|\otimes|-\rangle\langle -|)+(|+\rangle\langle +|\otimes|1\rangle\langle 1|)+(|-\rangle\langle -|\otimes|0\rangle\langle 0|)$

are two-qubit separable states with maximum correlations. Is this true? Is there a general notion for $n$ qubits?

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  • $\begingroup$ How did you construct $\rho$ ? $\endgroup$ – Frédéric Grosshans Jun 19 '12 at 9:09
  • $\begingroup$ I saw it mentioned in [link] prl.aps.org/abstract/PRL/v100/i5/e050502. (Also, I was missing a normalization factor). Intuitively, one can think of non-classical correlations as arising from having correlations between non-orthogonal states, as in the example. This state also has the property that its reduced states are completely mixed, like they are for maximally entangled states. $\endgroup$ – Juan Miguel Arrazola Jun 19 '12 at 14:30

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