Quantum Dynamical Entropies and Gács Algorithmic Entropy

Entropy

关键词: quantum spin chains;    algorithmic complexity;    dynamical entropy;   

DOI  :  10.3390/e14071259

来源: mdpi

【 摘 要 】

Several quantum dynamical entropies have been proposed that extend the classical Kolmogorov–Sinai (dynamical) entropy. The same scenario appears in relation to the extension of algorithmic complexity theory to the quantum realm. A theorem of Brudno establishes that the complexity per unit time step along typical trajectories of a classical ergodic system equals the KS-entropy. In the following, we establish a similar relation between the Connes–Narnhofer–Thirring quantum dynamical entropy for the shift on quantum spin chains and the Gács algorithmic entropy. We further provide, for the same system, a weaker linkage between the latter algorithmic complexity and a different quantum dynamical entropy proposed by Alicki and Fannes.

【 授权许可】

CC BY   
© 2012 by the author; licensee MDPI, Basel, Switzerland.