Geometric discord and Measurement-induced nonlocality for well known bound entangled states

Abstract

We employ geometric discord and measurement induced nonlocality to quantify non classical correlations of some well-known bipartite bound entangled states, namely the two families of Horodecki's ($2\otimes 4$, $3\otimes 3$ and $4\otimes 4$ dimensional) bound entangled states and that of Bennett etal's in $3\otimes 3$ dimension. In most of the cases our results are analytic and both the measures attain relatively small value. The amount of quantumness in the $4\otimes 4$ bound entangled state of Benatti etal and the $2\otimes 8$ state having the same matrix representation (in computational basis) is same. Coincidently, the $2m\otimes 2m$ Werner and isotropic states also exhibit the same property, when seen as $2\otimes 2m^2$ dimensional states.

V2: Title changed, one more state added; 11 pages (single column), 2 figures, accepted in Quantum Information Processing

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Cited by in corpus (10)

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• Quantum discord and its allies: a review
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• Fidelity Based Measurement Induced Nonlocality
• Qutrit geometric discord
• Quantum correlation induced by the average distance between the reduced states
• Fidelity based Measurement Induced Nonlocality and its dynamics in Quantum noisy channels
• Nonlocal Correlation in Heisenberg Spin Models
• Measurement-induced nonlocality in arbitrary dimensions in terms of the inverse approximate joint diagonalization
• Comment on "Sudden change in quantum discord accompanying the transition from bound to free entanglement"