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Physical Review A

Signatures of quantum fluctuations in the Dicke model by means of Rényi uncertainty

Manuel Calixto, Á. Nagy, I. Paradela, E. Romera

Published May 10, 2012• 36 citations
Publisher

Abstract

R'enyi uncertainty relations are shown to have significant importance in quantum phase transitions. They detect the quantum phase transition in the Dicke model. The R'enyi entropy sum is more appropriate for describing quantum fluctuations than the standard variance products.
DOI
10.1103/physreva.85.053813

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Entropy is a key concept of quantum information theory. The entropy of a quantum system is a measure of its randomness and has many applications in quantum communication protocols, quantum coherence, and so on. In this paper, based on the Rényi entropy and Tsallis entropy, we derive the bounds of the expectation value and variance of a quantum observable. By the maximal value of Rényi entropy, we show an upper bound on the product of variance and entropy. Furthermore, we obtain the reverse uncertainty relation for the product and sum of the variances for [Formula: see text] observables respectively.
\n\nIt is shown that there is a linear relation between the relative Rényi entropy and the density functional fidelity susceptibility. The derivative of the relative Rényi entropy with respect to the Rényi parameter α is also proportional to the density functional fidelity susceptibility. The benefit of these relations is illustrated for the Dicke model (considering a numerical study and a variational analytical approximation). These relations are useful to detect the second-order QPT in this model.\n