scholarly journals Classification of arbitrary multipartite entangled states under local unitary equivalence

2013 ◽  
Vol 46 (7) ◽  
pp. 075301 ◽  
Author(s):  
Jun-Li Li ◽  
Cong-Feng Qiao
Keyword(s):  
Entangled States ◽  
Unitary Equivalence ◽  
Local Unitary Equivalence

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 Classification of the entangled states of 2 ×N×N

2010 ◽  
Vol 43 (5) ◽  
pp. 055303 ◽  
Author(s):  
Shuo Cheng ◽  
Junli Li ◽  
Cong-Feng Qiao
Keyword(s):  
Entangled States

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 Persistent homology analysis of multiqubit entanglement

2020 ◽  
Vol 20 (5&6) ◽  
pp. 375-399
Author(s):  
Ricardo Mengoni ◽  
Alessandra Di Pierro ◽  
Leleh Memarzadeh ◽  
Stefano Mancini
Keyword(s):  
Persistent Homology ◽  
Occurrence Frequency ◽  
Entangled States ◽  
Data Sets ◽  
Bipartite Entanglement ◽  
Homology Analysis ◽  
Relative Occurrence ◽  
Associate State

We introduce a homology-based technique for the classification of multiqubit state vectors with genuine entanglement. In our approach, we associate state vectors to data sets by introducing a metric-like measure in terms of bipartite entanglement, and investigate the persistence of homologies at different scales. This leads to a novel classification of multiqubit entanglement. The relative occurrence frequency of various classes of entangled states is also shown.

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
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