First Passage Times for Continuous Quantum Measurement Currents
- URL: http://arxiv.org/abs/2308.07810v2
- Date: Wed, 6 Dec 2023 11:44:47 GMT
- Title: First Passage Times for Continuous Quantum Measurement Currents
- Authors: Michael J. Kewming, Anthony Kiely, Steve Campbell, Gabriel T. Landi
- Abstract summary: The First Passage Time (FPT) is the time taken for a process to reach a desired threshold.
In this letter we address the FPT of the measurement current in the case of continuously measured quantum systems.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The First Passage Time (FPT) is the time taken for a stochastic process to
reach a desired threshold. In this letter we address the FPT of the stochastic
measurement current in the case of continuously measured quantum systems. Our
approach is based on a charge-resolved master equation, which is related to the
Full-Counting statistics of charge detection. In the quantum jump unravelling
this takes the form of a coupled system of master equations, while for quantum
diffusion it becomes a type of quantum Fokker-Planck equation. In both cases,
we show that the FPT can be obtained by introducing absorbing boundary
conditions, making their computation extremely efficient {and analytically
tractable}. The versatility of our framework is demonstrated with two relevant
examples. First, we show how our method can be used to study the tightness of
recently proposed kinetic uncertainty relations (KURs) for quantum jumps, which
place bounds on the signal-to-noise ratio of the FPT. Second, we study the
usage of qubits as threshold detectors for Rabi pulses, and show how our method
can be employed to maximize the detection probability while, at the same time,
minimize the occurrence of false positives.
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