Reachability Analysis of Recursive Quantum Markov Chains

2013 ◽  
pp. 385-396 ◽  
Author(s):  
Yuan Feng ◽  
Nengkun Yu ◽  
Mingsheng Ying
Keyword(s):  
Markov Chains ◽  
Reachability Analysis ◽  
Quantum Markov Chains

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 Open quantum random walks, quantum Markov chains and recurrence

2019 ◽  
Vol 31 (07) ◽  
pp. 1950020 ◽  
Author(s):  
Ameur Dhahri ◽  
Farrukh Mukhamedov
Keyword(s):  
Markov Chains ◽  
Random Walks ◽  
Markov Processes ◽  
Transition Operator ◽  
Quantum Random Walks ◽  
Open Quantum ◽  
Commutative Subalgebra ◽  
Open Quantum Random Walks ◽  
Quantum Markov Chains

In the present paper, we construct QMCs (Quantum Markov Chains) associated with Open Quantum Random Walks such that the transition operator of the chain is defined by OQRW and the restriction of QMC to the commutative subalgebra coincides with the distribution [Formula: see text] of OQRW. This sheds new light on some properties of the measure [Formula: see text]. As an example, we simply mention that the measure can be considered as a distribution of some functions of certain Markov processes. Furthermore, we study several properties of QMC and associated measures. A new notion of [Formula: see text]-recurrence of QMC is studied, and the relations between the concepts of recurrence introduced in this paper and the existing ones are established.

scholarly journals Quantum Markov chains: A unification approach

2020 ◽  
Vol 23 (02) ◽  
pp. 2050016 ◽  
Author(s):  
Luigi Accardi ◽  
Abdessatar Souissi ◽  
El Gheteb Soueidy
Keyword(s):  
Markov Chains ◽  
Algebraic Property ◽  
Markov Property ◽  
Unified Approach ◽  
Local Algebras ◽  
Quantum Markov Chains

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.

Computation of mutual entropy in quantum markov chains

1994 ◽  
Vol 2 (3) ◽  
pp. 337-354 ◽  
Author(s):  
Luigi Accardi ◽  
Masanori Ohya ◽  
Hiroki Suyari
Keyword(s):  
Markov Chains ◽  
Mutual Entropy ◽  
Quantum Markov Chains
Sign in / Sign up

Export Citation Format

Share Document