scholarly journals Matrix product density operators: Renormalization fixed points and boundary theories

2017 ◽  
Vol 378 ◽  
pp. 100-149 ◽  
Author(s):  
J.I. Cirac ◽  
D. Pérez-García ◽  
N. Schuch ◽  
F. Verstraete
Keyword(s):  
Fixed Points ◽  
Matrix Product ◽  
Product Density ◽  
Density Operators

scholarly journals Efficient Description of Many-Body Systems with Matrix Product Density Operators

PRX Quantum ◽  
2020 ◽  
Vol 1 (1) ◽  
Author(s):  
Jiří Guth Jarkovský ◽  
András Molnár ◽  
Norbert Schuch ◽  
J. Ignacio Cirac
Keyword(s):  
Matrix Product ◽  
Many Body ◽  
Product Density ◽  
Density Operators ◽  
Many Body Systems

scholarly journals Simulating noisy quantum circuits with matrix product density operators

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Song Cheng ◽  
Chenfeng Cao ◽  
Chao Zhang ◽  
Yongxiang Liu ◽  
Shi-Yao Hou ◽  
...  
Keyword(s):  
Quantum Circuits ◽  
Matrix Product ◽  
Product Density ◽  
Density Operators

Global quantum discord and matrix product density operators

2018 ◽  
Vol 91 (6) ◽  
Author(s):  
Hai-Lin Huang ◽  
Hong-Guang Cheng ◽  
Xiao Guo ◽  
Duo Zhang ◽  
Yuyin Wu ◽  
...  
Keyword(s):  
Quantum Discord ◽  
Matrix Product ◽  
Product Density ◽  
Density Operators ◽  
Global Quantum Discord

scholarly journals Contractions of Product Density Operators of Systems of Identical Fermions and Bosons

2010 ◽  
Vol 2010 ◽  
pp. 1-26 ◽  
Author(s):  
Wiktor Radzki
Keyword(s):  
Thermodynamic Limit ◽  
Single Particle ◽  
Trace Class ◽  
Asymptotic Equivalence ◽  
Product Density ◽  
Expectation Values ◽  
Symmetric Products ◽  
Density Operators ◽  
Trace Class Operators ◽  
Explicit Formulae

Recurrence and explicit formulae for contractions (partial traces) of antisymmetric and symmetric products of identical trace class operators are derived. Contractions of product density operators of systems of identical fermions and bosons are proved to be asymptotically equivalent to, respectively, antisymmetric and symmetric products of density operators of a single particle, multiplied by a normalization integer. The asymptotic equivalence relation is defined in terms of the thermodynamic limit of expectation values of observables in the states represented by given density operators. For some weaker relation of asymptotic equivalence, concerning the thermodynamic limit of expectation values of product observables, normalized antisymmetric and symmetric products of density operators of a single particle are shown to be equivalent to tensor products of density operators of a single particle.

scholarly journals Separability for mixed states with operator Schmidt rank two

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 203 ◽  
Author(s):  
Gemma De las Cuevas ◽  
Tom Drescher ◽  
Tim Netzer
Keyword(s):  
Positive Semidefinite ◽  
Matrix Product ◽  
Mixed States ◽  
Product Density ◽  
Positive Semidefinite Matrices ◽  
Operator Systems ◽  
Minimum Number ◽  
Schmidt Rank ◽  
Elementary Tensor ◽  
Classical Correlations

The operator Schmidt rank is the minimum number of terms required to express a state as a sum of elementary tensor factors. Here we provide a new proof of the fact that any bipartite mixed state with operator Schmidt rank two is separable, and can be written as a sum of two positive semidefinite matrices per site. Our proof uses results from the theory of free spectrahedra and operator systems, and illustrates the use of a connection between decompositions of quantum states and decompositions of nonnegative matrices. In the multipartite case, we prove that any Hermitian Matrix Product Density Operator (MPDO) of bond dimension two is separable, and can be written as a sum of at most four positive semidefinite matrices per site. This implies that these states can only contain classical correlations, and very few of them, as measured by the entanglement of purification. In contrast, MPDOs of bond dimension three can contain an unbounded amount of classical correlations.

On $\alpha$-nonexpansive mapping and fixed-points in Banach spaces

2018 ◽  
Vol 2018 (-) ◽  
Author(s):  
Prondanai Kaskasem ◽  
Chakkrid Klin-eam ◽  
Suthep Suantai
Keyword(s):  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Banach Spaces

Fixed Points of Sequences of Mappings

2018 ◽  
Vol 2018 (-) ◽  
Author(s):  
C. Ganesa Moorthy ◽  
S. Iruthaya Raj
Keyword(s):  
Fixed Points
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