Dynamical Entropy Through Quantum Markov Chains

Yong‐Moon Park

Luigi Accardi, Masanori Ohya, Hiroki Suyari

Luigi Accardi, Masanori Ohya, Hiroki Suyari

Ameur Dhahri, Franco Fagnola

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.

Hiroki Suyari

Mutual entropy was introduced in classical communication theories to measure how much information can be transmitted from an input system to an output system. It has been expanded to quantum systems and applied to various physical models. By contrast, quantum Markov chains, introduced as an extension of classical Markov chains, have been used to explain the irreversibility of observed systems. In [1], a physical model used frequently in quantum optics was applied to a quantum Markov chain. The Stinespring-Kraus expression was derived to discuss mutual entropy on quantum Markov chains. Mutual entropy was then computed and irreversibility was examined using numerical experiments. To further the ongoing research, mean mutual entropy is applied here to the same quantum Markov chain as the previous one; necessary discussion is included. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(1): 104–112, 1997