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The Local Orthogonality Between Quantum States and Entanglement Decomposition

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In the paper, we show that when a quantum state can be decomposed as a convex combination of locally orthogonal mixed states, its entanglement can be decomposed into the entanglement of these mixed states without losing them. The obtained result generalizes a corresponding one proved by Horodecki (Acta Phys. Slov. 48, 141 1998). But, for the entanglement cost it requires certain conditions for holding the decomposition, and the distillable entanglement only has a week result as inequality. Finally, we presented an example to show that the conditions of our conclusions are existence.

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We want to express our heartfelt thanks to the referees for their important suggestions and remarks. This project is supported by Research Fund, Kumoh National Institute of Technology.

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Correspondence to Minhyung Cho.

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Kim, S., Wu, J., Zhang, L. et al. The Local Orthogonality Between Quantum States and Entanglement Decomposition. Int J Theor Phys 55, 2870–2881 (2016).

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