Non-Markovian dynamics of open quantum systems

Bi‐Heng Liu, Li Li, Yun‐Feng Huang +5 more

Daniel Klaus Burgarth, Paolo Facchi A, Marilena Ligabò +1 more

We show that non-Markovian open quantum systems can exhibit exact Markovian dynamics up to an arbitrarily long time; the non-Markovianity of such systems is thus perfectly ``hidden,'' i.e., not experimentally detectable by looking at the reduced dynamics alone. This shows that non-Markovianity is physically undecidable and extremely counterintuitive, since its features can change at any time, without precursors. Some interesting examples are discussed.

Z. Kanokov

Rahul Trivedi

Understanding and simulating non-Markovian quantum dynamics remains an important challenge in open quantum system theory. A key advance in this endeavour would be to develop a unified mathematical description of non-Markovian dynamics, and classify its complexity in the many-body setting. In this paper, we identify a general class of non-Markovian memory kernels, described by complex-valued radon measures, and define their dynamics through a regularization procedure constructing the corresponding system-environment unitary groups. Building on this definition, we then consider $k-$local many-body non-Markovian systems with physically motivated assumptions on the total variation and smoothness of the memory kernels. We establish that their dynamics can be efficiently approximated on quantum computers, thus providing a rigorous verification of the Extended Church-Turing thesis for this general class of non-Markovian open quantum systems.

Yusui Chen

Olli Siltanen, Tom Kuusela, Jyrki Piilo

We combine the dynamics of open quantum systems with interferometry and interference, introducing the concept of an open system interferometer. By considering a single photon in a Mach-Zehnder interferometer, where the polarization (open system) and frequency (environment) of the photon interact, we theoretically show that inside the interferometer, pathwise polarization dephasing dynamics is Markovian while the joint dynamics displays non-Markovian features. Outside the interferometer and due to interference, the open system displays rich dynamical features with distinct alternatives: only one path displays non-Markovian memory effects, both paths individually display them, or no memory effects appear at all. The scheme allows one to (1) probe the optical path difference inside the interferometer by studying pathwise non-Markovianity outside the interferometer, and (2) introduce pathwise dissipative features for the open system dynamics even though the system-environment interaction itself contains only dephasing. Due to the path dependencies, our results are tightly connected to quantum erasure. In general, our results open up alternative ways to control open system dynamics and for fundamental studies of quantum physics.