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Generalized Schmidt decomposition and classification of three-quantum-bit states

A. Acin·A. Andrianov·L. Costa·E. Jane·J. I. Latorre·R. Tarrach
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Abstract

We prove for any pure three-quantum-bit state the existence of local bases which allow to build a set of five orthogonal product states in terms of which the state can be written in a unique form. This leads to a canonical form which generalizes the two-quantum-bit Schmidt decomposition. It is uniquely characterized by the five entanglement parameters. It leads to a complete classification of the three-quantum-bit states. It shows that the right outcome of an adequate local measurement always erases all entanglement between the other two parties.

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A. Acin, A. Andrianov, L. Costa, E. Jane, J. I. Latorre, R. Tarrach. 2000-09-20. Generalized Schmidt decomposition and classification of three-quantum-bit states. https://doi.org/10.1103/physrevlett.85.1560

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