Process nonclassicality: characterization, canonical Hamiltonian ensemble representation, and quantification
Hong-Bin Chen1,2*, Ping-Yuan Lo3, Clemens Gneiting4, Joonwoo Bae5, Yueh-Nan Chen6,2, Franco Nori4,7
1Department of Engineering Science, National Cheng Kung University, Tainan, Taiwan
2Center for Quantum Frontiers of Research & Technology, National Cheng Kung University, Tainan, Taiwan
3Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan
4Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama, Japan
5School of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, Korea
6Department of Physics, National Cheng Kung University, Tainan, Taiwan
7Physics Department, University of Michigan, Ann Arbor, USA
* Presenter:Hong-Bin Chen,
The characterization, explanation, and quanti cation 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 non-dissipative 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 classifi cation towards quantifying the nonclassicality of pure dephasing dynamics. In the spirit of the Wigner function, we generalize Hamiltonian ensembles to encompass quasi-probability distributions comprising negative values. By using Lie algebra representations, Fourier transforms on groups, and root space decompositions, we achieve to overcome the difficulty of pinning down the uniqueness of quasi-probability distributions, provided diagonal member Hamiltonians, and therefore lift such distributions as 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 classical probability distributions. We illustrate our method for qubit, qutrit, and qubit-pair pure dephasing and demonstrate how to implement our approach with quantum process tomography and quantum state tomography experiments.

Keywords: Hamiltonian ensemble, Process nonclassicality, Measure of nonclassicality, Dephasing, Lie algebra