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

2000/03/31 by A. Acín, A. Acin, A. Andrianov +8 · 21 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph

paper · pdf · doi:10.1103/physrevlett.85.1560

published as Phys. Rev. Lett. 85 (2000) 1560 · 4 pages, Revtex. Published version, minor changes and new references added

openalex publication_date 2000/08/14 · arxiv created 2000/09/20 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01

Abstract

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.

Citations

• Three qubits can be entangled in two inequivalent ways
• Higher order Schmidt decompositions
• Zur Theorie der linearen und nichtlinearen Integralgleichungen
• Distributed Entanglement

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