AQP Seminar: Full counting statistics of information fluctuations and the optimum capacity

Aalto Quantum Physics -seminaari (Nanotalo). Puhuja: Prof. Yasuhiro Utsumi (Department of Physics Engineering, Mie University, Japan)

Through a mesoscopic quantum conductor, one bit of information content can be conveyed by the arrival or non-arrival of an electron. The performance of communication through such conductor is limited by laws of physics and has been discussed since 1960s [1,2]. The optimum channel capacity, the maximum rate at which information can be transmitted under a given signal power, i.e. heat current, relates the theory of communication, thermodynamics and quantum physics [2]. We revisit this issue by considering a quantum conductor and analyzing fluctuations of self-information associated with the reduced density matrix of a detector (drain) lead subjected to a constraint of the local heat quantity [3]. In this talk, we briefly summarize the theory of information channel capacity by Shannon [1]. Then we evaluate the probability distribution of self-information of electron occupation probabilities in the drain lead by exploiting the multi-contour Keldysh technique [4]. We present a Jarzynski-equality like universal relation, that relates the optimum capacity, the Renyi entropy of order 0, and the number of integer partitions. We apply our theory to a two terminal quantum dot and analyze the probability distributions. We point out that at the steady-state, the reduced density matrix and the operator of the local heat quantity of the subsystem may be commutative.

[1] C.E. Shannon, A Mathematical Theory of Communication, Bell System Techn. J. 27 370-423, 623-656 (1948).
[2] R. Landauer, Science, 272, 1914 (1996); S. Lloyd, Nature, 406, 1047 (2000). 
[3] Y. Utsumi, Phys. Rev. B 99, 115310 (2019). 
[4] Yu. V. Nazarov, Phys. Rev. B 84, 205437 (2011); M. H. Ansari and Yu. V. Nazarov, Phys. Rev. B 91, 104303 (2015); Phys. Rev. B 91, 174307 (2015); M. H. Ansari, Phys. Rev. B 95, 174302 (2017).