Local Unitary Equivalence of Multipartite Pure States

2009/09/28 by Barbara Kraus, B. Kraus · 1 citation
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.104.020504

published as Phys. Rev. Lett. 104, 020504 (2010) · 5 pages

arxiv created 2009/09/28 · openalex publication_date 2010/01/14 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Necessary and sufficient conditions for the equivalence of arbitrary n-qubit pure quantum states under local unitary (LU) operations are derived. First, an easily computable standard form for multipartite states is introduced. Two generic states are shown to be LU equivalent iff their standard forms coincide. The LU-equivalence problem for nongeneric states is solved by presenting a systematic method to determine the LU operators (if they exist) which interconvert the two states.

Citations

• Three qubits can be entangled in two inequivalent ways
• Entanglement versus Correlations in Spin Systems
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Generalized Schmidt Decomposition and Classification of Three-Quantum-Bit States
• Entanglement in many-body systems
• Distributed Entanglement
• Quantum entanglement

Cited by

• Quantum entanglement [wikipedia]