Eur. Phys. J. Special Topics 227, 1911–1928 (2019)
https://doi.org/10.1140/epjst/e2018-800043-4

Review

Full counting statistics of information content

Department of Physics Engineering, Faculty of Engineering, Mie University, Tsu, Mie 514-8507, Japan

^a e-mail: utsumi@phen.mie-u.ac.jp

Received: 10 April 2018
Received in final form: 19 June 2018
Published online: 18 January 2019

Abstract

We review connections between the cumulant generating function of full counting statistics of particle number and the Rényi entanglement entropy. We calculate these quantities based on the fermionic and bosonic path-integral defined on multiple Keldysh contours. We relate the Rényi entropy with the information generating function, from which the probability distribution function of self-information is obtained in the nonequilibrium steady state. By exploiting the distribution, we analyze the information content carried by a single bosonic particle through a narrow-band quantum communication channel. The ratio of the self-information content to the number of bosons fluctuates. For a small boson occupation number, the average and the fluctuation of the ratio are enhanced.