Quantum Dynamical Entropy for Completely Positive Map

Abstract

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.

On Entropy of Quantum Compound Systems

“…In this section, we briefly explain the definition of the KOW entropy according to [19]. Based on the C*-mixing entropy and the compound states on general quantum systems, the mean entropy and mean mutual entropies were discussed in [22,23,35].…”

“…for any A ∈ B ⊗ A. in the sense of [2,19], where ω ∈ S (K) and ϕ ∈ S (H) are density operators associated to ω and ϕ. The dual map E * ,ω of E ,ω is a lifting from…”

“…The classical dynamical entropy was discussed in [17] with respect to a measure preserving transformation. The quantum dynamical entropy was studied by several authors [2,3,3,4,[6][7][8][9][10]12,13,15,16,19,29,31,34,35].…”

Quantum Entropy and Its Applications to Quantum Communication and Statistical Physics

“…A dynamical entropy (Kossakowski, Ohya and Watanabe) [59] for not only a shift but also a completely positive (CP) map is defined by generalizing the entropy defined through quantum Markov chain and AF entropy defined by a finite operational partition.…”

“…(2) It is defined through the quantum Markov chain (QMC) was done in [58]. (3) The dynamical entropy for a completely positive (CP) maps was introduced in [59].…”