منابع مشابه
Robustness of quantum Markov chains
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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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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Quantum Analogues of Markov Chains Name: Ashwin Nayak, Peter C. Richter, Mario Szegedy Affil./Addr. 1: Department of Combinatorics and Optimization, and Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada. Email: [email protected] Affil./Addr. 2: Department of Computer Science, Rutgers, the State University of New Jersey, Piscataway, NJ, USA. Email: {richterp,s...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2007
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-007-0362-8