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Generalized Schmidt Decomposition and Classification of Three-Quantum-Bit States

2000; American Physical Society; Volume: 85; Issue: 7 Linguagem: Inglês

10.1103/physrevlett.85.1560

1092-0145

A. Acín, A. A. Andrianov, Laura Costa, E. Jané, José I. Latorre, R. Tarrach,

Quantum Mechanics and Applications

We prove for any pure three-quantum-bit state the existence of local bases which allow one 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.