Clustering Property of Quantum Markov Chain Associated to XY-model with Competing Ising Interactions on the Cayley Tree of Order Two

2019 ◽  
Vol 22 (1) ◽  
Author(s):  
Farrukh Mukhamedov ◽  
Soueidy El Gheteb
Keyword(s):  
Markov Chain ◽  
Cayley Tree ◽  
Xy Model ◽  
Quantum Markov Chain ◽  
Clustering Property

Uniqueness of Quantum Markov Chain Associated with XY-Ising Model on Cayley Tree of Order Two

2017 ◽  
Vol 24 (02) ◽  
pp. 1750010 ◽  
Author(s):  
Farrukh Mukhamedov ◽  
Soueidy El Gheteb
Keyword(s):  
Markov Chain ◽  
Ising Model ◽  
Markov Chains ◽  
Boundary Conditions ◽  
Finite Volume ◽  
Cayley Tree ◽  
Limit State ◽  
Weak Limit ◽  
Quantum Markov Chain ◽  
Quantum Markov Chains

In this paper, we consider backward and forward Quantum Markov Chains (QMC) associated with XY -Ising model on the Cayley tree of order two. We construct finite volume states with boundary conditions, and define QMC as a weak limit of those states which depend on the boundary conditions. We prove that the limit state is a unique QMC associated with such a model, this means the QMC does not depend on the boundary conditions. Moreover, we observe the relation between backward and forward QMC.

scholarly journals A quantum Markov chain approach to phase transitions for quantum Ising model with competing XY-interactions on a Cayley tree

2020 ◽  
Vol 61 (9) ◽  
pp. 093505
Author(s):  
Farrukh Mukhamedov ◽  
Abdessatar Barhoumi ◽  
Abdessatar Souissi ◽  
Soueidy El Gheteb
Keyword(s):  
Markov Chain ◽  
Phase Transitions ◽  
Ising Model ◽  
Cayley Tree ◽  
Quantum Markov Chain ◽  
Markov Chain Approach ◽  
Quantum Ising Model

Factors Generated by XY-Model with Competing Ising Interactions on the Cayley Tree

2019 ◽  
Vol 21 (1) ◽  
pp. 241-253 ◽  
Author(s):  
Farrukh Mukhamedov ◽  
Soueidy El Gheteb
Keyword(s):  
Cayley Tree ◽  
Xy Model

scholarly journals ON QUANTUM MARKOV CHAINS ON CAYLEY TREE I: UNIQUENESS OF THE ASSOCIATED CHAIN WITH XY-MODEL ON THE CAYLEY TREE OF ORDER TWO

2011 ◽  
Vol 14 (03) ◽  
pp. 443-463 ◽  
Author(s):  
LUIGI ACCARDI ◽  
FARRUKH MUKHAMEDOV ◽  
MANSOOR SABUROV
Keyword(s):  
Markov Chains ◽  
Boundary Conditions ◽  
Cayley Tree ◽  
Weak Limit ◽  
Finite Volumes ◽  
Xy Model ◽  
Quantum Markov Chains

In this paper we study forward quantum Markov chains (QMC) defined on Cayley tree. A construction of such QMC is provided, namely we construct states on finite volumes with boundary conditions, and define QMC as a weak limit of those states which depends on the boundary conditions. Using the provided construction, we investigate QMC associated with XY-model on a Cayley tree of order two. We prove uniqueness of QMC associated with such a model, this means the QMC does not depend on the boundary conditions.

scholarly journals Uniqueness of quantum Markov chains associated with an XY-model on a cayley tree of order 2

2011 ◽  
Vol 90 (1-2) ◽  
pp. 162-174 ◽  
Author(s):  
L. Accardi ◽  
F. M. Mukhamedov ◽  
M. Kh. Saburov
Keyword(s):  
Markov Chains ◽  
Cayley Tree ◽  
Xy Model ◽  
Quantum Markov Chains

QUANTUM DYNAMICAL ENTROPY FOR COMPLETELY POSITIVE MAP

1999 ◽  
Vol 02 (02) ◽  
pp. 267-282 ◽  
Author(s):  
A. KOSSAKOWSKI ◽  
M. OHYA ◽  
N. WATANABE
Keyword(s):  
Markov Chain ◽  
Completely Positive Map ◽  
Completely Positive ◽  
Positive Map ◽  
Quantum Markov Chain ◽  
Quantum Dynamical ◽  
Dynamical Entropy

A dynamical entropy for not only shift but also completely positive (CP) map is defined by generalizing the AOW entropy1 defined through quantum Markov chain and AF entropy defined by a finite operational partition. Our dynamical entropy is numerically computed for several models.

scholarly journals QUANTUM HITTING TIME ON THE COMPLETE GRAPH

2010 ◽  
Vol 08 (05) ◽  
pp. 881-894 ◽  
Author(s):  
RAQUELINE AZEVEDO MEDEIROS SANTOS ◽  
RENATO PORTUGAL
Keyword(s):  
Markov Chain ◽  
Complete Graph ◽  
Quantum Algorithms ◽  
Success Probability ◽  
Natural Extension ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Hitting Time ◽  
Quantum Markov Chain ◽  
Definition Of

Quantum walks play an important role in the area of quantum algorithms. Many interesting problems can be reduced to searching marked states in a quantum Markov chain. In this context, the notion of quantum hitting time is very important, because it quantifies the running time of the algorithms. Markov chain-based algorithms are probabilistic, therefore the calculation of the success probability is also required in the analysis of the computational complexity. Using Szegedy's definition of quantum hitting time, which is a natural extension of the definition of the classical hitting time, we present analytical expressions for the hitting time and success probability of the quantum walk on the complete graph.

scholarly journals A MODEL FOR QUANTUM QUEUE

2013 ◽  
Vol 11 (02) ◽  
pp. 1350023 ◽  
Author(s):  
PIOTR GAWRON ◽  
DARIUSZ KURZYK ◽  
ZBIGNIEW PUCHAŁA
Keyword(s):  
Markov Chain ◽  
Numerical Analysis ◽  
Discrete Time ◽  
Quantum Model ◽  
Queueing Model ◽  
Discrete Time Markov Chain ◽  
Quantum Markov Chain ◽  
Quantum Domain ◽  
Time Quantum

We consider an extension of discrete time Markov chain queueing model to the quantum domain by use of discrete time quantum Markov chain. We introduce methods for numerical analysis of such models. Using these tools we show that quantum model behaves fundamentally different from the classical one.

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