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• W3100582382 abstract "The problem of the detection statistics of a quantum walker has received increasing interest, connected as it is to the problem of quantum search. We investigate the effect of employing a moving detector, using a projective measurement approach with fixed sampling time $tau$, with the detector moving right before every detection attempt. For a tight-binding quantum walk on the line, the moving detector allows one to target a specific range of group velocities of the walker, qualitatively modifying the behavior of the quantum first-detection probabilities. We map the problem to that of a stationary detector with a modified unitary evolution operator and use established methods for the solution of that problem to study the first-detection statistics for a moving detector on a finite ring and on an infinite 1D lattice. On the line, the system exhibits a dynamical phase transition at a critical value of $tau$, from a state where detection decreases exponentially in time and the total detection is very small, to a state with power-law decay and a significantly higher probability to detect the particle. The exponent describing the power-law decay of the detection probability at this critical $tau$ is 10/3, as opposed to 3 for every larger $tau$. In addition, the moving detector strongly modifies the Zeno effect." @default.
• W3100582382 created "2020-11-23" @default.
• W3100582382 creator A5074511334 @default.
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• W3100582382 date "2019-08-02" @default.
• W3100582382 modified "2023-09-24" @default.
• W3100582382 title "Running measurement protocol for the quantum first-detection problem" @default.
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• W3100582382 doi "https://doi.org/10.1088/1751-8121/ab3305" @default.
• W3100582382 hasPublicationYear "2019" @default.
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