After a short introduction to the Algebraic formulation of classical stochastic processes and fields, we extend to the quantum case the notion of expected classical Markov field and we prove the equivalence of several formulations of the multi-dimensional Markov property. To this goal we need a Kadison-Schwarz inequality for completely positive maps on *-algebras which is proved in the appendix.
The Expected Markov Property for Quantum Markov Fields
A. Dhahri
2023-01-01
Abstract
After a short introduction to the Algebraic formulation of classical stochastic processes and fields, we extend to the quantum case the notion of expected classical Markov field and we prove the equivalence of several formulations of the multi-dimensional Markov property. To this goal we need a Kadison-Schwarz inequality for completely positive maps on *-algebras which is proved in the appendix.File in questo prodotto:
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