Quantifying the nonclassicality of pure dephasing

Hong-Bin Chen, Ping-Yuan Lo, Clemens Gneiting, Joonwoo Bae, Yueh-Nan Chen, Franco Nori

Published 2018-11-22Version 1

The characterization, explanation, and quantification of quantumness, in particular the discrimination from classicality in terms of classical strategies, lie at the heart of quantum physics. Dephasing processes, caused by the information exchange between a quantum system and its environment, play a central role in that respect, as they control the transition between the quantum and the classical realm. Recently, it is shown that dephasing dynamics itself can exhibit classical or nonclassical traits, depending on the nature of the system-environment correlations and the related (im)possibility to simulate these dynamics with Hamiltonian ensembles---the classical strategy. Here we propose to extend this classification towards {\it quantifying} the nonclassicality of pure dephasing dynamics. In the spirit of Wigner's function, we generalize Hamiltonian ensembles to encompass quasi-probability distributions comprising negative values. Based on Lie algebra representations, Fourier transforms on groups, and root space decompositions, we demonstrate that quasi-probability distributions are faithful representations of pure dephasing dynamics; moreover, we show how to retrieve these quasi-probability distributions. This allows us to quantify process-nonclassicality time-independently, in terms of the deviations of the corresponding quasi-probability distributions from legitimate (non-negative) probability distributions. We exemplify our method along qubit, qutrit, and qubit-pair pure dephasing.