Abstract
In this work, we study the Rényi entropies of quantum states for bosons in the phase-space representation. With the help of the Bopp rule, we derive the entropies of Gaussian states in closed form for positive integers and then, with the help of the analytic continuation, acquire the closed form also for real values of . The quantity , primarily studied in the literature, will then be a special case of our finding. Subsequently we acquire the Rényi entropies, with positive integers , in closed form also for a specific class of the non-Gaussian states (mixed states) for bosons, which may be regarded as a generalization of the eigenstates (pure states) of a single harmonic oscillator with , in which the Wigner functions have negative values indeed. Due to the fact that the dynamics of a system consisting of oscillators is Gaussian, our result will contribute to a systematic study of the Rényi entropy dynamics when the current form of a non-Gaussian state is initially prepared.
- Received 16 April 2018
- Revised 24 May 2018
DOI:https://doi.org/10.1103/PhysRevE.97.062141
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