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:1101.5736 · Chinese Physics Letters

Local Unitary Equivalent Consistence for n -Party States and Their (n − 1)-Party Reduced Density Matrices

Zhen Wang, Heping Wang, Zhi‐Xi Wang, Shao-Ming Fei

Published Feb 1, 2011• 5 citations
arXivHTMLPDF

Abstract

We present that the local unitary equivalence of n-party pure states is consistent with that of their (n − 1)-party reduced density matrices. As an application, we obtain the local invariants for a class of tripartite pure qudits.
DOI
10.1088/0256-307x/28/2/020302

Related papers

EQUIVALENCE OF TRIPARTITE QUANTUM STATES UNDER LOCAL UNITARY TRANSFORMATIONS

Sergio A Albeverio, LAURA CATTANEO, Shao-Ming Fei +1 more

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.

arXiv:quant-ph/0512246•International Journal of Quantum Information•Dec 1, 2005•32 citations

Pure tripartite entanglement types based on spectra of reduced density matrices

Saeid Molladavoudi, Hishamuddin B Zainuddin, Chan Kar Tim

Given a specific ordered spectra of (shifted) one-qubit reduced density matrices, we discuss that the pure tripartite entanglement for a system consisting of three qubits is determined by only two local unitary invariant polynomials.

Journal of Physics Conference Series•Nov 19, 2014•0 citations

Characterizing local unitary equivalence of multipartite states by local unitary Bargmann invariants

Yi Shen, Lin Chen, Shao-Ming Fei

Local unitary (LU) equivalent states are crucial for understanding the structure of quantum entanglement. We investigate the LU equivalence based on the LU Bargmann invariants (LUBIs). We consider for which states the LUBIs are sufficient to ensure the LU equivalence. We focus on a class of multipartite states with complete local commutativity, called CLC states. We first show that for multipartite CLC states, all the LUBIs are sufficient to ensure the local permutation equivalence, if their single-party marginals are diagonal and non-degenerate. By virtue of the fact that the CLC property remains unchanged under local operations, we verify that the LUBIs are also sufficient to ensure the LU equivalence of multipartite CLC states whose single-party marginals are non-degenerate. Furthermore, when the single-party marginals are degenerate, we propose concrete examples of two-qudit and three-qubit systems, showing that there are states which share all the LUBIs but are not LU equivalent.

quant-pharXiv:2609.22902•Sep 22, 2026•0 citations

Multipartite states under local unitary transformations

Sergio A Albeverio, Cattaneo, L, Fei, S M +1 more

The equivalence problem under local unitary transformation for $n$--partite pure states is reduced to the one for $(n-1)$--partite mixed states. In particular, a tripartite system $\\mathcal{H}_A\\otimes\\mathcal{H}_B\\otimes\\mathcal{H}_C$, where $\\mathcal{H}_j$ is a finite dimensional complex Hilbert space for $j=A,B,C$, is considered and a set of invariants under local transformations is introduced, which is complete for the set of states whose partial trace with respect to $\\mathcal{H}_A$ belongs to the class of generic mixed states.

•Jan 1, 2005•17 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

Necessary and sufficient conditions for local unitary equivalence of multiqubit states

Ana María Guerra Martins

We derive the necessary and sufficient conditions for the local unitary (LU) equivalence of two general (pure or mixed) $n$-qubit states and determine the local unitary operators connecting them. Almost all relevant information is contained in the one-qubit reduced matrices of the multiqubit states under investigation. Our technique relies on identifying ab initio all local symmetries and the corresponding local cyclic unitary operators. To derive the above conditions we use the reference forms of the multiqubit states whose definition requires the diagonalization of the one-qubit reduced matrices. Based on those conditions, we propose a straightforward protocol to decide whether or not two $n$-qubit states are LU equivalent.

arXiv:1408.3840•Physical Review A•Apr 8, 2015•17 citations
Local unitary (LU) equivalent states are crucial for understanding the structure of quantum entanglement. We investigate the LU equivalence based on the LU Bargmann invariants (LUBIs). We consider for which states the LUBIs are sufficient to ensure the LU equivalence. We focus on a class of multipartite states with complete local commutativity, called CLC states. We first show that for multipartite CLC states, all the LUBIs are sufficient to ensure the local permutation equivalence, if their single-party marginals are diagonal and non-degenerate. By virtue of the fact that the CLC property remains unchanged under local operations, we verify that the LUBIs are also sufficient to ensure the LU equivalence of multipartite CLC states whose single-party marginals are non-degenerate. Furthermore, when the single-party marginals are degenerate, we propose concrete examples of two-qudit and three-qubit systems, showing that there are states which share all the LUBIs but are not LU equivalent.
The equivalence problem under local unitary transformation for nnn--partite pure states is reduced to the one for (n−1)(n-1)(n−1)--partite mixed states. In particular, a tripartite system mathcalHAotimesmathcalHBotimesmathcalHC\\mathcal{H}_A\\otimes\\mathcal{H}_B\\otimes\\mathcal{H}_CmathcalHA​otimesmathcalHB​otimesmathcalHC​, where mathcalHj\\mathcal{H}_jmathcalHj​ is a finite dimensional complex Hilbert space for j=A,B,Cj=A,B,Cj=A,B,C, is considered and a set of invariants under local transformations is introduced, which is complete for the set of states whose partial trace with respect to mathcalHA\\mathcal{H}_AmathcalHA​ belongs to the class of generic mixed states.
We derive the necessary and sufficient conditions for the local unitary (LU) equivalence of two general (pure or mixed) nnn-qubit states and determine the local unitary operators connecting them. Almost all relevant information is contained in the one-qubit reduced matrices of the multiqubit states under investigation. Our technique relies on identifying ab initio all local symmetries and the corresponding local cyclic unitary operators. To derive the above conditions we use the reference forms of the multiqubit states whose definition requires the diagonalization of the one-qubit reduced matrices. Based on those conditions, we propose a straightforward protocol to decide whether or not two nnn-qubit states are LU equivalent.