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Quantum Markov chains and classical random sequences

Published online by Cambridge University Press:  22 January 2016

Yun-Gang Lu
Yun-Gang Lu*
Affiliation:
Dipartimento di Matematica, Università di Bari, Centro V. Volterra Università di Roma II
*
Università degli Studi di Bari, Dipartimento di Matematica, Campus Universitario Via E. Orabona 4
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Quantum Markov chain introduced by Accardi (cf. [1,2,3]) is one of natural generalization of classical Markov chain. It has many interesting applications in physics and the most important one is given by the paper of Fannes-Nachtergaele-Werner ([4]), where an application of quantum Markov chain’s technique enables us to understand the Valence bond states well.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 139 , September 1995 , pp. 173 - 183
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1995

References

[ 1 ] Accardi, L., On the noncommutative Markovian property, Funct. Anal. Appl., 9 (1975), 1–8.Google Scholar
[ 2 ] Accardi, L., Noncommutative Markov Chains, In: International School of Math. Phys. Camerino, (1974), 268–295.Google Scholar
[ 3 ] Accardi, L., Topics in quantum probability, Phy. Reports, 77, No. 3 (1981), 169–192.Google Scholar
[ 4 ] Fannes, M., Nachtergaele, B., Werner, R. F., Valence bond states on quantum spin chains as ground states with spectral gap, J. Phys. A: Math. Gen., 24 (1991), 185–190.Google Scholar