Quantum Markov chains: A unification approach
نویسندگان
چکیده
منابع مشابه
Approximate quantum Markov chains
This chapter reviews the concept of a Markov chain for random variables and then introduces a generalization to quantummechanical systems. We discuss the subtle differences between classical and quantumMarkov chains and point out difficulties that show up in the quantum case. Unlike the classical case that has been analyzed and understood well in the past, certain aspects of quantumMarkov chain...
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A new approach to quantum Markov chains is presented. We first define a transition operation matrix (TOM) as a matrix whose entries are completely positive maps whose column sums form a quantum operation. A quantum Markov chain is defined to be a pair (G, E) where G is a directed graph and E = [Eij ] is a TOM whose entry Eij labels the edge from vertex j to vertex i. We think of the vertices of...
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A framework for finite-dimensional quantum Markov chains on Hilbert spaces is introduced. Quantum Markov chains generalize both classical Markov chains with possibly hidden states and existing models of quantum walks on finite graphs. Quantum Markov chains are based on Markov operations that may be applied to quantum systems and include quantum measurements, for example. It is proved that quant...
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If the conditional information of a classical probability distribution of three random variables is zero, then it obeys a Markov chain condition. If the conditional information is close to zero, then it is known that the distance (minimum relative entropy) of the distribution to the nearest Markov chain distribution is precisely the conditional information. We prove here that this simple situat...
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Article history: Received 10 May 2012 Received in revised form 28 November 2012 Accepted 22 April 2013 Available online 25 April 2013
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ژورنال
عنوان ژورنال: Infinite Dimensional Analysis, Quantum Probability and Related Topics
سال: 2020
ISSN: 0219-0257,1793-6306
DOI: 10.1142/s0219025720500162