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Journal of Physics A Mathematical and Theoretical

Entanglement entropy in extended quantum systems

Pasquale Calabrese, John Cardy, Benjamin Doyon

Published Dec 2, 2009• 367 citations
Publisher

Abstract

Full text of this Introduction is given in the pdf provided
DOI
10.1088/1751-8121/42/50/500301

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In classical information theory, the most important theorems are the coding theorems, which were discussed by calculating the mean entropy and the mean mutual entropy defined by the classical dynamical entropy (Kolmogorov–Sinai). The quantum dynamical entropy was first studied by Emch [13] and Connes–Stormer [11]. After that, several approaches for introducing the quantum dynamical entropy were proposed [10,[Formula: see text]3,[Formula: see text]8,[Formula: see text]39,[Formula: see text]15,[Formula: see text]44,[Formula: see text]9,[Formula: see text]27,[Formula: see text]28,[Formula: see text]2,[Formula: see text]19,[Formula: see text]45]. The efficiency of information transmission for the quantum processes is investigated by using the von Neumann entropy [22] and the Ohya mutual entropy [24]. These entropies were extended to S-mixing entropy by Ohya [26,[Formula: see text]27] in general quantum systems. The mean entropy and the mean mutual entropy for the quantum dynamical systems were introduced based on the S-mixing entropy. In this paper, based on research into the dynamical entropy and mean mutual entropy of quantum systems, this study investigates the characteristics of quantum channels that exhibit entanglement, a property unique to quantum systems, and investigates the behaviour of quantum entropy for compound quantum channels by changing the perspective from information transmission between input and output to a new perspective of information transmission from the initial state to the final state.
We investigate the emerging properties of quantum walks with temporal disorder engineered from a binary Markov chain with tailored correlation, C, and disorder strength, r. We show that when the disorder is weak-[Formula: see text]-the introduction of negative correlation leads to a counter-intuitive higher production of spin-lattice entanglement entropy, [Formula: see text], than the setting with positive correlation, that is [Formula: see text]. These results show that negatively correlated disorder plays a more important role in quantum entanglement than it has been assumed in the literature.