Characterizing Non-Markovian Dynamics

William C. Saslaw

Kai-Hung Wang, Shih-Hsuan Chen, Yu‐Cheng Lin +1 more

The way a principle system and its environment interact characterizes the non-Markovianity of the dynamics. Herein, we investigate the non-Markovian dynamics of photon polarization in a birefringent crystal. We consider the so-called ``quantity of quantum-mechanical process'' first defined by Hsieh et al. [Sci. Rep. 7, 13588 (2017)]. The non-Markovianity of the photon dynamics is evaluated by examining the quantity of quantum-mechanical process varying with time, and the difference between the quantity of quantum-mechanical process in a complete dynamics and that in a process composed of two subprocesses. We show that all of the processes identified as Markovian in the seminal study of Liu et al. [Nat. Phys. 7, 931 (2011)] can actually be identified as non-Markovian. The presented method enables us to classify non-Markovianity in the dynamical processes that are classified as Markovian by existing verification criteria. Overall, the results confirm the feasibility of performing the experimental characterization of photon dynamics using an all-optical setup and provide a useful insight into enhancing the accuracy and control of quantum system designs for quantum engineering applications.

Vasyl A. Alba, Gordon J Berman, William Bialek +1 more

Dariusz Chruściński

We analyze classes of legitimate quantum dynamics using a local in time master equation. Markovian dynamics is characterized in terms of a divisible dynamical map. Moreover, we provide a family of criteria which can distinguish Markovian and non-Markovian quantum evolution. They are based on a simple observation that Markovian dynamics implies monotonic behavior of several well-known quantities such as distinguishability of states, fidelity and relative entropy.

K. El Anouz, Abderrahim El Allati, NASSER METWALLY

Ryan S. Bennink, Pavel Lougovski

Abstract Established methods for characterizing quantum information processes do not capture non-Markovian (history-dependent) behaviors that occur in real systems. These methods model a quantum process as a fixed map on the state space of a predefined system of interest. Such a map averages over the system’s environment, which may retain some effect of its past interactions with the system and thus have a history-dependent influence on the system. Although the theory of non-Markovian quantum dynamics is currently an active area of research, a systematic characterization method based on a general representation of non-Markovian dynamics has been lacking. In this article we present a systematic method for experimentally characterizing the dynamics of open quantum systems. Our method, which we call quantum process identification (QPI), is based on a general theoretical framework which relates the (non-Markovian) evolution of a system over an extended period of time to a time-local (Markovian) process involving the system and an effective environment. In practical terms, QPI uses time-resolved tomographic measurements of a quantum system to construct a dynamical model with as many dynamical variables as are necessary to reproduce the evolution of the system. Through numerical simulations, we demonstrate that QPI can be used to characterize qubit operations with non-Markovian errors arising from realistic dynamics including control drift, coherent leakage, and coherent interaction with material impurities.