scholarly journals Local unitary equivalence of quantum states and simultaneous orthogonal equivalence

2016 ◽  
Vol 57 (6) ◽  
pp. 062205
Author(s):  
Naihuan Jing ◽  
Min Yang ◽  
Hui Zhao
Keyword(s):  
Quantum States ◽  
Unitary Equivalence ◽  
Local Unitary Equivalence

scholarly journals Local unitary equivalence of arbitrary dimensional bipartite quantum states

2012 ◽  
Vol 86 (1) ◽  
Author(s):  
Chunqin Zhou ◽  
Ting-Gui Zhang ◽  
Shao-Ming Fei ◽  
Naihuan Jing ◽  
Xianqing Li-Jost
Keyword(s):  
Quantum States ◽  
Unitary Equivalence ◽  
Local Unitary Equivalence

scholarly journals Local unitary equivalence of multiqubit mixed quantum states

2014 ◽  
Vol 89 (6) ◽  
Author(s):  
Ming Li ◽  
Tinggui Zhang ◽  
Shao-Ming Fei ◽  
Xianqing Li-Jost ◽  
Naihuan Jing
Keyword(s):  
Quantum States ◽  
Unitary Equivalence ◽  
Local Unitary Equivalence

scholarly journals On Local Unitary Equivalence of Two and Three-qubit States

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Bao-Zhi Sun ◽  
Shao-Ming Fei ◽  
Zhi-Xi Wang
Keyword(s):  
Unitary Equivalence ◽  
Local Unitary Equivalence ◽  
Qubit States

scholarly journals Deciding unitary equivalence between matrix polynomials and sets of bipartite quantum states

2011 ◽  
Vol 11 (9&10) ◽  
pp. 813-819
Author(s):  
Eric Chitambar ◽  
Carl Miller ◽  
Yaoyun Shi
Keyword(s):  
Success Probability ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Quantum States ◽  
Unitary Equivalence ◽  
Matrix Polynomials ◽  
Unitary Transformations ◽  
The Matrix ◽  
Pure States ◽  
High Success Probability

In this brief report, we consider the equivalence between two sets of $m+1$ bipartite quantum states under local unitary transformations. For pure states, this problem corresponds to the matrix algebra question of whether two degree $m$ matrix polynomials are unitarily equivalent; i.e. $UA_iV^\dagger=B_i$ for $0\leq i\leq m$ where $U$ and $V$ are unitary and $(A_i, B_i)$ are arbitrary pairs of rectangular matrices. We present a randomized polynomial-time algorithm that solves this problem with an arbitrarily high success probability and outputs transforming matrices $U$ and $V$.

scholarly journals Symmetric states: local unitary equivalence via stabilizers

2010 ◽  
Vol 10 (11&12) ◽  
pp. 1029-1041
Author(s):  
Curt D. Cenci ◽  
David W. Lyons ◽  
Laura M. Snyder ◽  
Scott N. Walck
Keyword(s):  
Degrees Of Freedom ◽  
Rotation Group ◽  
Equivalence Classes ◽  
Unitary Equivalence ◽  
Finite Subgroups ◽  
Local Unitary Equivalence ◽  
Symmetric States

We classify local unitary equivalence classes of symmetric states via a classification of their local unitary stabilizer subgroups. For states whose local unitary stabilizer groups have a positive number of continuous degrees of freedom, the classification is exhaustive. We show that local unitary stabilizer groups with no continuous degrees of freedom are isomorphic to finite subgroups of the rotation group $SO(3)$, and give examples of states with discrete stabilizers.

scholarly journals Criterion of local unitary equivalence for multipartite states

2013 ◽  
Vol 88 (4) ◽  
Author(s):  
Ting-Gui Zhang ◽  
Ming-Jing Zhao ◽  
Ming Li ◽  
Shao-Ming Fei ◽  
Xianqing Li-Jost
Keyword(s):  
Unitary Equivalence ◽  
Local Unitary Equivalence ◽  
Multipartite States
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