Running Measurement Protocol for the Quantum First-detection problem

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.

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Cited by in corpus (6)

• Preface: New trends in first-passage methods and applications in the life sciences and engineering
• Quantum unitary evolution interspersed with repeated non-unitary interactions at random times: The method of stochastic Liouville equation, and two examples of interactions in the context of a tight-binding chain
• The first detection time of a quantum state under random probing
• Quantum random walk and tight-binding model subject to projective measurements at random times
• Optimal Measurement Protocols in Quantum Zeno Effect
• Purely quantum memory in closed systems observed via imperfect measurements