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Entanglement measures and the Hilbert-Schmidt distance

Masanao Ozawa
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Abstract

In order to construct a measure of entanglement on the basis of a ``distance'' between two states, it is one of desirable properties that the ``distance'' is nonincreasing under every completely positive trace preserving map. Contrary to a recent claim, this letter shows that the Hilbert-Schmidt distance does not have this property.

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Masanao Ozawa. 2000-02-13. Entanglement measures and the Hilbert-Schmidt distance. https://doi.org/10.1016/s0375-9601(00)00171-7

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