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arxiv: 1205.0592 · v1 · pith:B2KKE76Tnew · submitted 2012-05-03 · 🪐 quant-ph · math.OA

Optimal PPTES witnesses for states in mathbb C^notimes mathbb C^n

classification 🪐 quant-ph math.OA
keywords witnessesoptimalentanglementmathbbpartialpptespropertyspanning
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Recently, X. Qi and J. Hou [Phys. Rev. A 85, 022334 (2012)] provided optimal entanglement witnesses without the spanning property. These witnesses are associated to indecomposable positive linear maps, but it is not checked whether partial transposes of these witnesses are also optimal. We show that partial transposes of these entanglement witnesses have spanning property, and these witnesses are indeed optimal PPTES witnesses (non-decomposable optimal entanglement witnesses).

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