Quest for optimal quantum resetting: protocols for a particle on a chain

Abstract

In the classical context, it is well known that, sometimes, if the search does not find its target, it is better to start the process anew again, known as resetting. The quantum counterpart of resetting also indicates speeding up the detection process by eliminating the dark states, i.e., situations where the particle avoids detection. In this work, we introduce the most probable position resetting(MPR) protocol in which, at a given resetting step, resets are done with certain probabilities to the set of possible peak positions (where the probability of finding the particle is maximum) that could occur because of the previous resets and followed by uninterrupted unitary evolution, irrespective of which path was taken by the particle in previous steps. In a tight-binding lattice model, there exists a 2-fold degeneracy (left and right) of the positions of maximum probability. The survival probability with optimal restart rate approaches zero (detection probability approaches one) when the particle is reset with equal probability on both sides path independently. This protocol significantly reduces the optimal mean first-detected-passage time (FDT) and performs better even if the detector is far apart compared to the usual resetting protocols where the particle is brought back to the initial position. We propose a modified protocol, an adaptive two-stage MPR, by making the associated probabilities of going to the right and left a function of steps. In this protocol, we see a further reduction of the optimal mean FDT and improvement in the search process when the detector is far apart.