Quantum Markov Processes

1980 ◽  
pp. 87-97 ◽  
Author(s):  
Luigi Accardi
Keyword(s):  
Markov Processes ◽  
Quantum Markov Processes

scholarly journals CLASSICAL MARKOV PROCESSES FROM QUANTUM LÉVY PROCESSES

1999 ◽  
Vol 02 (01) ◽  
pp. 105-129 ◽  
Author(s):  
UWE FRANZ
Keyword(s):  
Markov Process ◽  
Hopf Algebra ◽  
Markov Processes ◽  
Lévy Processes ◽  
Sufficient Conditions ◽  
Markov Property ◽  
Vacuum State ◽  
Levy Processes ◽  
Quantum Process ◽  
Quantum Markov Processes

We show how classical Markov processes can be obtained from quantum Lévy processes. It is shown that quantum Lévy processes are quantum Markov processes, and sufficient conditions for restrictions to subalgebras to remain quantum Markov processes are given. A classical Markov process (which has the same time-ordered moments as the quantum process in the vacuum state) exists whenever we can restrict to a commutative subalgebra without losing the quantum Markov property.8 Several examples, including the Azéma martingale, with explicit calculations are presented. In particular, the action of the generator of the classical Markov processes on polynomials or their moments are calculated using Hopf algebra duality.

scholarly journals Absorption in Invariant Domains for Semigroups of Quantum Channels

2021 ◽  
Author(s):  
Raffaella Carbone ◽  
Federico Girotti
Keyword(s):  
Hilbert Space ◽  
Ergodic Theory ◽  
Markov Processes ◽  
Separable Hilbert Space ◽  
Quantum Channels ◽  
Quantum Markov Processes ◽  
Positive Recurrent ◽  
Markov Evolution ◽  
Absorption Probabilities ◽  
Invariant Domains

AbstractWe introduce a notion of absorption operators in the context of quantum Markov processes. The absorption problem in invariant domains (enclosures) is treated for a quantum Markov evolution on a separable Hilbert space, both in discrete and continuous times: We define a well-behaving set of positive operators which can correspond to classical absorption probabilities, and we study their basic properties, in general, and with respect to accessibility structure of channels, transience and recurrence. In particular, we can prove that no accessibility is allowed between the null and positive recurrent subspaces. In the case, when the positive recurrent subspace is attractive, ergodic theory will allow us to get additional results, in particular about the description of fixed points.

scholarly journals The χ2-divergence and mixing times of quantum Markov processes

2010 ◽  
Vol 51 (12) ◽  
pp. 122201 ◽  
Author(s):  
K. Temme ◽  
M. J. Kastoryano ◽  
M. B. Ruskai ◽  
M. M. Wolf ◽  
F. Verstraete
Keyword(s):  
Markov Processes ◽  
Mixing Times ◽  
Quantum Markov Processes

scholarly journals MARKOV STATES AND CHAINS ON THE CAR ALGEBRA

2007 ◽  
Vol 10 (02) ◽  
pp. 165-183 ◽  
Author(s):  
LUIGI ACCARDI ◽  
FRANCESCO FIDALEO ◽  
FARRUH MUKHAMEDOV
Keyword(s):  
Markov Chains ◽  
Tensor Product ◽  
Markov Processes ◽  
Car Algebra ◽  
Quantum Markov Processes ◽  
Canonical Anticommutation Relations ◽  
Satisfactory Theory ◽  
Quantum Markov Chains ◽  
General Method

We introduce the notion of Markov states and chains on the Canonical Anticommutation Relations algebra over ℤ, emphasizing some remarkable differences with the infinite tensor product case. We describe the structure of the Markov states on this algebra and show that, contrarily to the infinite tensor product case, not all these states are diagonalizable. A general method to construct nontrivial quantum Markov chains on the CAR algebra is also proposed and illustrated by some pivotal examples. This analysis provides a further step for a satisfactory theory of quantum Markov processes.

scholarly journals Preparation of entangled states by quantum Markov processes

2008 ◽  
Vol 78 (4) ◽  
Author(s):  
B. Kraus ◽  
H. P. Büchler ◽  
S. Diehl ◽  
A. Kantian ◽  
A. Micheli ◽  
...  
Keyword(s):  
Markov Processes ◽  
Entangled States ◽  
Quantum Markov Processes

scholarly journals Spectral Convergence Bounds for Classical and Quantum Markov Processes

2014 ◽  
Vol 333 (2) ◽  
pp. 565-595 ◽  
Author(s):  
Oleg Szehr ◽  
David Reeb ◽  
Michael M. Wolf
Keyword(s):  
Markov Processes ◽  
Spectral Convergence ◽  
Quantum Markov Processes
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