Quest for optimal quantum resetting: Protocols for a particle on a chain.

Area of Science:

• Quantum physics
• Quantum information science
• Statistical mechanics

Background:

• Classical resetting involves restarting a search process to improve efficiency.
• Quantum resetting aims to accelerate detection by avoiding dark states, where particles evade detection.

Purpose of the Study:

• Introduce a novel quantum resetting protocol: Most Probable Position Resetting (MPR).
• Investigate MPR's effectiveness in reducing detection time compared to traditional resetting methods.
• Explore an adaptive two-stage MPR for further optimization.

Main Methods:

• Developed the Most Probable Position Resetting (MPR) protocol.
• Applied MPR to a tight-binding lattice model with twofold degeneracy in peak positions.
• Analyzed survival probability and first-detected-passage time (FDT) with varying reset rates.
• Introduced and analyzed an adaptive two-stage MPR protocol.

Main Results:

• MPR protocol, with optimal restart rates, drives survival probability to 0 (detection probability to 1).
• MPR significantly reduces the optimal mean first-detected-passage time (FDT).
• MPR demonstrates superior performance, especially for distant detectors, compared to resetting to the initial position.
• The adaptive two-stage MPR further reduces optimal mean FDT and enhances search efficiency for distant detectors.

Conclusions:

• MPR is an effective strategy for accelerating quantum detection processes.
• The adaptive two-stage MPR offers enhanced performance for optimizing search times in quantum systems.
• Resetting to most probable positions is a more efficient strategy than resetting to the origin.