Abstract

We consider a bipartite quantum conductor and discuss fluctuations of self-information asso-ciated with the reduced density matrix of a subsystem subjected to a constraint of the local heat quantity. The operator of the self-information introduced in this way can be regarded as the en-tanglement Hamiltonian subjected to the constraint of the local heat quantity. We utilize this quantity to analyze the quantum limit of information transmission through the quantum con-ductor. By exploiting the multi-contour Keldysh technique, we calculate the Renyi entropy, or the information generating function, from which the probability distribution of the conditional self-information is derived. We present an equality, that relates the optimum capacity of infor-mation transmission between the subsystems and the Renyi entropy of order 0, which is the number of eigenvalues of the entanglement Hamiltonian and is, for fermions, the number of integer partitions into distinct parts. 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] Y. Utsumi, Phys. Rev. B 96, 085304 (2017)
[2] Y. Utsumi, Phys. Rev. B 92, 165312 (2015)