Causality, localisation, and universality of monitored quantum walks with long-range hopping

• URL: http://arxiv.org/abs/2504.12053v1
• Date: Wed, 16 Apr 2025 13:08:42 GMT
• Title: Causality, localisation, and universality of monitored quantum walks with long-range hopping
• Authors: Sayan Roy, Shamik Gupta, Giovanna Morigi,
• Abstract summary: We show that the optimal resetting rate depends on the size of the lattice and diverges as $alphato 0$.<n>We derive simple models reproducing the numerical results, shedding light on the interplay of long-range coherent dynamics, symmetries, and local quantum measurement processes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum resetting protocols can speed up the time in which a quantum walker reaches a target site on a lattice. In these setups, a detector monitors the target site and the walker motion is restarted if the detector has not clicked after a fixed time interval. The optimal resetting rate can be extracted from the time evolution of the probability $S(t)$ that the detector has not clicked up to time $t$. We analyse $S(t)$ for a quantum walk in a one-dimensional lattice when the coupling between sites decays algebraically as $d^{-\alpha}$ with the distance $d$, for $\alpha\in(0,\infty)$. At long-times, $S(t)$ decays with a universal power-law exponent that is independent of $\alpha$. At short times, $S(t)$ exhibits a plethora of phase transitions as a function of $\alpha$. These lead to the identification of two main regimes for the optimal resetting rate. For $\alpha>1$, the resetting rate $r$ is bounded from below by the velocity with which information propagates causally across the lattice. For $\alpha<1$, instead, the long-range hopping tends to localise the walker: The optimal resetting rate depends on the size of the lattice and diverges as $\alpha\to 0$. We derive simple models reproducing the numerical results, shedding light on the interplay of long-range coherent dynamics, symmetries, and local quantum measurement processes in determining equilibrium. Our predictions can be verified in existing experimental setups.

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