Untitled

Abstract

Classical dynamical entropy is an important tool to analyze communication processes. For instance, it may represent a transmission capacity for one letter. In this paper, we formulate the notion of dynamical entropy through a quantum Markov chain and calculate it for some simple models.

Non-homogeneous quantum Markov states and quantum Markov fields

“…Then it is easy to verify that the new sequence {E j } j − ≤j<j + is made of conditional expectations and satisfies (6). Hence, taking into account the above considerations, we can conclude that the set of Markov states w.r.t.…”

“…It can be shown (see (25)) that, if ϕ is a locally faithful Markov state w.r.t. the sequence of transition expectations {E j }, then {E j } must satisfy (6).…”

“…Because of condition (6), the E α can be extended to conditional expectations (which we continue to call E α ) on all of A. Such extensions satisfy the projectivity condition…”

“…Hamiltonians relative to pairwise interactions), was vastly developed in the last decades. Concerning this point, the reader is referred to [6,9,13,17] and the literature cited therein.…”

Aspectos asintóticos y geométricos del caos cuántico

“…Para una descripción cuántica de los sistemas caóticos, necesitaríamos una extensión cuántica de la entropía-KS. En este sentido existen varios candidatos no conmutativos [61,62,63,64,65] con la presencia de un rango temporal finito donde la versión clásica y cuántica coinciden, hecho que es considerado como la principal peculiaridad del caos cuántico [1].…”