Quantum Markov chains: A unification approach

被引：28

作者：

Accardi, Luigi ^{[1
]}

Souissi, Abdessatar ^{[2
,3
]}

Soueidy, El Gheteb ^{[4
]}

机构：

[1] Univ Roma Tor Vergata, Ctr Interdipartimentale Vito Volterra, Via Columbia 2, I-00133 Rome, Italy

[2] Qassim Univ, Coll Business Management, Dept Accounting, Ar Rass, Saudi Arabia

[3] Carthage Univ, Preparatory Inst Sci & Tech Studies, La Marsa, Tunisia

[4] Nouakchott Univ, Dept Math, Nouakchott, Mauritania

来源：

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 2020年 / 23卷 / 02期

关键词：

Ordered products; quantum Markov chains; extendability; transition expectations; STATES;

D O I：

10.1142/S0219025720500162

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study a unified approach for quantum Markov chains (QMCs). A new quantum Markov property that generalizes the old one, is discussed. We introduce Markov states and chains on general local algebras, possessing a generic algebraic property. We stress that this kind of algebras includes both Boson and Fermi algebras. Our main results concern two reconstruction theorems for quantum Markov chains and for quantum Markov states. Namely, we illustrate the results through examples.

引用

页数：24

共 20 条

[1]

ACCARDI L, 1983, P ROY IRISH ACAD A, V83, P251

[2] On the EPR-chameleon experiment [J].

Accardi, L ;

Imafuku, K ;

Regoli, M .

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2002, 5 (01) :1-20

[3] CONDITIONAL EXPECTATIONS IN VONNEUMANN-ALGEBRAS AND A THEOREM OF TAKESAKI [J].

ACCARDI, L ;

CECCHINI, C .

JOURNAL OF FUNCTIONAL ANALYSIS, 1982, 45 (02) :245-273

[4]

Accardi L, 1987, LECT NOTES MATH, V1396, P73

[5]

Accardi L., 1975, Func. Anal. Appl, V9, P1

[6] Markov states and chains on the CAR algebra [J].

Accardi, Luigi ;

Fidaleo, Francesco ;

Mukhamedov, Farruh .

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2007, 10 (02) :165-183

[7] Entangled Markov chains [J].

Accardi, Luigi ;

Fidaleo, Francesco .

ANNALI DI MATEMATICA PURA ED APPLICATA, 2005, 184 (03) :327-346

[8] Identification of the theory of orthogonal polynomials in d-indeterminates with the theory of 3-diagonal symmetric interacting Fock spaces on Cd [J].

Accardi, Luigi ;

Barhoumi, Abdessatar ;

Dhahri, Ameur .

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2017, 20 (01)

[9] On Quantum Markov Chains on Cayley Tree II: Phase Transitions for the Associated Chain with XY-Model on the Cayley Tree of Order Three [J].

Accardi, Luigi ;

Mukhamedov, Farrukh ;

Saburov, Mansoor .

ANNALES HENRI POINCARE, 2011, 12 (06) :1109-1144

[10] Quantum Markov Model for Data from Shafir-Tversky Experiments in Cognitive Psychology [J].

Accardi, Luigi ;

Khrennikov, Andrei ;

Ohya, Masanori .

OPEN SYSTEMS & INFORMATION DYNAMICS, 2009, 16 (04) :371-385

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