Potential theory for quantum Markov states and other quantum Markov chains

被引：2
|
作者：
Dhahri, Ameur [1 ]
Fagnola, Franco [1 ]
机构：
[1] Politecn Milan, Dipartimento Matemat, Piazza Leonardo Vinci 32, I-20133 Milan, Italy
来源：
ANALYSIS AND MATHEMATICAL PHYSICS | 2023年 / 13卷 / 02期
关键词：
Quantum Markov chains; Potential; Recurrence; Transience;
D O I：
10.1007/s13324-023-00790-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We introduce a potential theory for a class of Quantum Markov Chains whose forward and backward Markov transition operators satisfy a special composition rule. We study the associated recurrence, transient and irreducibility properties and we prove that an irreducible quantum Markov chain is either recurrent or transient. Moreover, we show that our theory applies in many cases such as: quantum random walks, diagonal states, entangled Quantum Markov Chains. A characterization of Entangled Quantum Markov Chains is also given.
引用
收藏
页数：21
相关论文
共 50 条
  • [1] Potential theory for quantum Markov states and other quantum Markov chains
    Ameur Dhahri
    Franco Fagnola
    Analysis and Mathematical Physics, 2023, 13
  • [2] Decoherence in quantum Markov chains
    Medeiros Santos, Raqueline Azevedo
    Portugal, Renato
    Fragoso, Marcelo Dutra
    QUANTUM INFORMATION PROCESSING, 2014, 13 (02) : 559 - 572
  • [3] Decoherence in quantum Markov chains
    Raqueline Azevedo Medeiros Santos
    Renato Portugal
    Marcelo Dutra Fragoso
    Quantum Information Processing, 2014, 13 : 559 - 572
  • [4] Recurrence of a class of quantum Markov chains on trees
    Barhoumi, Abdessatar
    Souissi, Abdessatar
    CHAOS SOLITONS & FRACTALS, 2022, 164
  • [5] Open Quantum Random Walks and Quantum Markov Chains
    A. Dhahri
    F. Mukhamedov
    Functional Analysis and Its Applications, 2019, 53 : 137 - 142
  • [6] Open Quantum Random Walks and Quantum Markov Chains
    Dhahri, A.
    Mukhamedov, F.
    FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2019, 53 (02) : 137 - 142
  • [7] Model checking quantum Markov chains
    Feng, Yuan
    Yu, Nengkun
    Ying, Mingsheng
    JOURNAL OF COMPUTER AND SYSTEM SCIENCES, 2013, 79 (07) : 1181 - 1198
  • [8] Quantum Markov chains: A unification approach
    Accardi, Luigi
    Souissi, Abdessatar
    Soueidy, El Gheteb
    INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2020, 23 (02)
  • [9] Open quantum random walks, quantum Markov chains and recurrence
    Dhahri, Ameur
    Mukhamedov, Farrukh
    REVIEWS IN MATHEMATICAL PHYSICS, 2019, 31 (07)
  • [10] Mean mutual entropy in quantum Markov chains
    Suyari, H
    ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE, 1997, 80 (01): : 104 - 112
12345