Dynamical entropy of generalized quantum Markov chains

Luigi Accardi, Masanori Ohya, Noboru Watanabe

Luigi Accardi, Masanori Ohya, Hiroki Suyari

Luigi Accardi, Masanori Ohya, Hiroki Suyari

Farrukh Maksutovich Mukhamedov

Yong‐Moon Park, Hyun Hye Shin

We compute the dynamical entropy in the sense of Connes, Narnhofer, and Thirring of generalized quantum Markov chain over infinite dimensional algebras. For the case in which the transition expectation is defined by a set of conditional density amplitudes, we show that the dynamical entropy is equal to the mean entropy. Thus we extend the result of Park [Lett. Math. Phys. 32, 63–74 (1994)] to non-AF type quantum Markov chains. We employ the main method developed in Park [Lett. Math. Phys. 32, 63–74 (1994)] with necessary modifications.

Andrzej Kossakowski, Makoto Ohya, N. WATANABE

A dynamical entropy for not only shift but also completely positive (CP) map is defined by generalizing the AOW entropy1 defined through quantum Markov chain and AF entropy defined by a finite operational partition. Our dynamical entropy is numerically computed for several models.