TY - JOUR

T1 - Running measurement protocol for the quantum first-detection problem

AU - Meidan, Dror

AU - Barkai, Eli

AU - Kessler, David A.

N1 - Publisher Copyright:
© 2019 Institute of Physics Publishing. All rights reserved.

PY - 2019/8/2

Y1 - 2019/8/2

N2 - The problem of the detection statistics of a quantum walker has received increasing interest. We investigate the effect of employing a moving detector, using a projective measurement approach with fixed sampling time, 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 from a state where the probability of detection decreases exponentially in time and the total detection probability is very small, to a state with power-law decay and a significantly higher total probability to detect the particle. The exponent describing the power-law decay of the detection probability at this critical is 10/3, as opposed to 3 for every larger In addition, the moving detector strongly modifies the Zeno effect. 2019 IOP Publishing Ltd.

AB - The problem of the detection statistics of a quantum walker has received increasing interest. We investigate the effect of employing a moving detector, using a projective measurement approach with fixed sampling time, 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 from a state where the probability of detection decreases exponentially in time and the total detection probability is very small, to a state with power-law decay and a significantly higher total probability to detect the particle. The exponent describing the power-law decay of the detection probability at this critical is 10/3, as opposed to 3 for every larger In addition, the moving detector strongly modifies the Zeno effect. 2019 IOP Publishing Ltd.

KW - first passage

KW - quantum walk

KW - renewal equation

UR - http://www.scopus.com/inward/record.url?scp=85072380708&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/ab3305

DO - 10.1088/1751-8121/ab3305

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SN - 1751-8113

VL - 52

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 35

M1 - 354001

ER -