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 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.

Classification of the entangled states 2 × M × N

2012 ◽  
Vol 12 (1) ◽  
pp. 251-268 ◽  
Author(s):  
Jun-Li Li ◽  
Cong-Feng Qiao
Keyword(s):  
Entangled States

MIXED-STATE ENTANGLEMENT IN THE LIGHT OF PURE-STATE ENTANGLEMENT CONSTRAINED BY SUPERSELECTION RULES

2005 ◽  
Vol 03 (supp01) ◽  
pp. 145-153
Author(s):  
STEPHEN D. BARTLETT ◽  
HOWARD. M. WISEMAN ◽  
ROBERT W. SPEKKENS ◽  
ANDREW C. DOHERTY
Keyword(s):  
Mixed State ◽  
Pure State ◽  
Entangled States ◽  
Quantum Operations ◽  
Local Quantum ◽  
Bound Entanglement ◽  
Quantum Optical

We show that the classification of bi-partite pure entangled states when local quantum operations are restricted, e.g., constrained by local superselection rules, yields a structure that is analogous in many respects to that of mixed-state entanglement, including such exotic phenomena as bound entanglement and activation. This analogy aids in resolving several conceptual puzzles in the study of entanglement under restricted operations. Specifically, we demonstrate that several types of quantum optical states that possess confusing entanglement properties are analogous to bound entangled states. Also, the classification of pure-state entanglement under restricted operations can be much simpler than for mixed state entanglement. For instance, in the case of local Abelian superselection rules all questions concerning distillability can be resolved.

scholarly journals Braiding quantum gates from partition algebras

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 311
Author(s):  
Pramod Padmanabhan ◽  
Fumihiko Sugino ◽  
Diego Trancanelli
Keyword(s):  
Statistical Mechanics ◽  
Braid Group ◽  
Quantum Gates ◽  
Entangled States ◽  
Baxter Equation ◽  
Classical Communication ◽  
Qubit System ◽  
Partition Algebras

Unitary braiding operators can be used as robust entangling quantum gates. We introduce a solution-generating technique to solve the (d,m,l)-generalized Yang-Baxter equation, for m/2≤l≤m, which allows to systematically construct such braiding operators. This is achieved by using partition algebras, a generalization of the Temperley-Lieb algebra encountered in statistical mechanics. We obtain families of unitary and non-unitary braiding operators that generate the full braid group. Explicit examples are given for a 2-, 3-, and 4-qubit system, including the classification of the entangled states generated by these operators based on Stochastic Local Operations and Classical Communication.

Classification of the entangled states of $$2 \times L \times M \times N$$ 2 × L × M × N

2014 ◽  
Vol 14 (1) ◽  
pp. 229-245 ◽  
Author(s):  
Liang-Liang Sun ◽  
Jun-Li Li ◽  
Cong-Feng Qiao
Keyword(s):  
Entangled States
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