Stochastic resetting induces quantum non-Markovianity

Abstract

Stochastic resetting describes dynamics which are reinitialized to a reference state at random times. These protocols are attracting significant interest: they can stabilize nonequilibrium stationary states, generate correlations in noninteracting systems, and enable optimal search strategies. While a constant reset probability results in a Markovian dynamics, much less is known about non-Markovian effects in quantum stochastic resetting. Here, we analyze memory effects in these processes -- examining the evolution of quantum states and of observables -- through witnesses of non-Markovianity for open quantum systems. We focus on discrete-time reset processes, which are of particular interest as they can be implemented on existing gate-operated quantum devices. We show that these processes are generically described by non-divisible maps and, in non-classical scenarios where the effective reset probability can become negative, can feature revivals in the state distinguishability. Our results reveal non-Markovian effects in quantum stochastic resetting and show that a time-dependent reset may be exploited to engineer enhanced stationary quantum correlations.

Figures (3)

• Figure 1: Quantum stochastic resetting and non-Markovianity. (a) At any discrete time, the system state $\rho$ evolves via a Kraus map $\mathcal{E}$ or resets to a reference state $\rho_{\rm reset}$. The latter event is characterized by a reset probability $r(t)$, where $t$ is the time from the previous reset event. In genuinely quantum reset processes, $r(t)$ can assume negative values as it can happen to rates in continuous-time open quantum dynamics chruscinski2022. (b) We explore non-Markovianity by analyzing non-monotonic behavior of certain quantities under the stochastic resetting dynamics.
• Figure 2: P-divisibility of dynamical maps. (a) We consider $100$ random Hermitian operators $X$ propagated, in the Schrödinger picture, via randomly generated reset processes (see main text). Their trace norm is mostly decreasing with, however, positive increments $\Delta(t)$ highlighting that $\Phi(t)$ is not P-divisible in general. (b) We generate, as in a), random operators and processes and analyze the Heisenberg evolution. The norm $\|\Phi^*(t)[X]\|$ shows more prominent non-monotonic behavior [see positive values of the increment $\delta(t)$], witnessing that also $\Phi^*(t)$ cannot be generally P-divisible.
• Figure 3: Engineering stationary correlations with non-Markovian reset. (a) Concurrence $\mathcal{C}$ in the stationary state of a Markovian stochastic resetting, as a function of the interaction strength $V$ and of the reset probability $r$. Here, $\Omega=3$. (b) For the exemplary cases $V=1$ and $V=2$, we show that a time-dependent choice $r(t)$ can recover a stationary bipartite entanglement (see dashed lines) which is higher than the one achieved by any possible Markovian stochastic resetting (solid lines).