Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0512246 · International Journal of Quantum Information

EQUIVALENCE OF TRIPARTITE QUANTUM STATES UNDER LOCAL UNITARY TRANSFORMATIONS

Sergio A Albeverio, LAURA CATTANEO, Shao-Ming Fei, Xiaohong Wang

Published Dec 1, 2005• 32 citations
arXivHTMLPDF

Abstract

The equivalence of tripartite pure states under local unitary transformations is investigated. The nonlocal properties for a class of tripartite quantum states in ℂK ⊗ ℂM ⊗ ℂN composite systems are investigated and a complete set of invariants under local unitary transformations for these states is presented. It is shown that two of these states are locally equivalent if and only if all these invariants have the same values.

DOI
10.1142/s0219749905001481

Related papers

Local Invariants for a Class of Tripartite Quantum Mixed States

Xiaohong Wang

We study the equivalence of tripartite mixed states under local unitary transformations. The nonlocal properties for a class of tripartite quantum states in ℂ K ⊗ℂ M ⊗ℂ N composite systems are investigated and a complete set of invariants under local unitary transformations for these states is presented. It is shown that two of these states are locally equivalent if and only if all these invariants have the same values.

Communications in Theoretical Physics•Feb 1, 2006•1 citation

Local unitary equivalence of arbitrary dimensional bipartite quantum states

Chunqin Zhou, Ting-Gui Zhang, Shao-Ming Fei +2 more

The nonlocal properties of arbitrary dimensional bipartite quantum systems are investigated. A complete set of invariants under local unitary transformations is presented. These invariants give rise to both sufficient and necessary conditions for the equivalence of quantum states under local unitary transformations: two density matrices are locally equivalent if and only if all these invariants have equal values.

arXiv:1207.2688•Physical Review A•Jul 11, 2012•32 citations

Local Equivalence for a Class of Bipartite Quantum Mixed States

X. H. Wang, Sergio A Albeverio, L. Cattaneo +1 more

We study the equivalence of bipartite mixed states under local unitary transformations. A complete set of invariants under local unitary transformations is presented for a class of mixed states in CM ⊗ CN composite systems. It is shown that two density matrices in this class are locally equivalent if and only if all these invariants have equal values for these density matrices.

AIP conference proceedings•Jan 1, 2007•0 citations

A complete set of local invariants for a family of multipartite mixed states

Xiaohong Wang, Shao-Ming Fei, Ke Wu

We study the equivalence of quantum states under local unitary transformations by using the singular value decomposition. A complete set of invariants under local unitary transformations is presented for several classes of tripartite mixed states in KxMxN composite systems. Two density matrices in the same class are equivalent under local unitary transformations if and only if all these invariants have equal values for these density matrices.

arXiv:0801.1706•Journal of Physics A Mathematical and Theoretical•Dec 19, 2007•1 citation

Invariants for a Class of Nongeneric Three-Qubit States

Sun Bao-Zhi, Fei Shao-Ming

We investigate the equivalence of quantum states under local unitary transformations. A complete set of invariants under local unitary transformations are presented for a class of non-generic three-qubit mixed states. It is shown that two such states in this class are locally equivalent if and only if all these invariants have equal values for them.

arXiv:quant-ph/0606148•Communications in Theoretical Physics•Jun 1, 2006•4 citations

Local equivalence of rank-2 quantum mixed states

Sergio A Albeverio, Shao-Ming Fei, Debashish Goswami

We investigate the equivalence of quantum mixed states under local unitary transformations. For a class of rank-2 mixed states, a sufficient and necessary condition of local equivalence is obtained by giving a complete set of invariants under local unitary transformations, such that two states in this class are locally equivalent if and only if all these invariants have equal values for them.

arXiv:0711.1210•Journal of Physics A Mathematical and Theoretical•Aug 21, 2007•7 citations
The equivalence of tripartite pure states under local unitary transformations is investigated. The nonlocal properties for a class of tripartite quantum states in ℂK ⊗ ℂM ⊗ ℂN composite systems are investigated and a complete set of invariants under local unitary transformations for these states is presented. It is shown that two of these states are locally equivalent if and only if all these invariants have the same values.