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

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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.

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ACÍN DAL MASCHIO, Antonio, et al. Generalized Schmidt decomposition and classification of three-quantum-bit states. Physical Review Letters. 2000. Vol. 85, num. 7, pags. 1560-1563. ISSN 0031-9007. [consulted: 31 of May of 2026]. Available at: https://hdl.handle.net/2445/12805

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