Quantum of information and its fluctuations in a conductor heat current*

Mesoscopic quantum conductors have been tools to investigate thermodynamics in the quantum regime [1]. They also offer a playground to think about entanglement and information transmission. In a quantum conductor, by applying a source-drain bias voltage, entangled electron-hole pairs can be created [2]. Moreover one bit of information content can be conveyed by the arrival or non-arrival of an electron [3]. We revisit this problem by analyzing a novel quantity, the distribution of fluctuating information, particle and heat currents, which is closely related to the `Rényi entanglement entropy’ [4]. Our approach is the full-counting statistics based on the multi-contour Keldysh Green function developed recently [4,5].
To quantify the particle-hole entanglement, one has to remove the contribution from superpositions of different particle number eigenstates, which cannot be created and measured locally [2]. For this purpose, we account for the local electron number constraint and discuss the condition that the maximum accessible entanglement is realized [4].
The quantum physics limits the performance of communication through a conductor [3]. The optimum channel capacity, the maximum rate at which information can be transmitted under a given signal power, i.e. heat current, relates theory of communication and thermodynamics. We demonstrate a universal relation connecting the fluctuation of information, the Rényi entropy of order zero and the optimum capacity [4].

[1] JP Pekola, Nat. Phys. 11 118 (2015)
[2] CWJ Beenakker, Proc. Int. School of Physics Enrico Fermi, 162 (2006); HM Wiseman, et al., PRL 91 097902 (2003)
[3] CM Caves, et al., Rev. Mod. Phys. 66 481 (1994); MP Blencowe, et al., PRA 62 052104 (2000)
[4] Y Utsumi, PRB 96 085304 (2017); ibid. 92 165312 (2015); arXiv:1807.04338
[5] YV Nazarov, PRB 84 205437 (2011); MH Ansari and YV Nazarov, ibid. 91 104303 (2015); ibid. 91 174307 (2015); ibid. 95 174302 (2017)