Imagine an experiment where a quantum particle inside a box is released at some time in some initial state. A detector is placed at a fixed location inside the box and its clicking signifies arrival of the particle at the detector. What is the time of arrival (TOA) of the particle at the detector ? Within the paradigm of the measurement postulate of quantum mechanics, one can use the idea of projective measurements to define the TOA. We consider a setup where a detector keeps making instantaneous measurements at regular finite time intervals until it detects the particle at time t , which is defined as the TOA. This is a stochastic variable and, for a simple lattice model of a free particle in a one-dimensional box, we find interesting features such as power-law tails in its distribution and in the probability of survival (non-detection). We propose a perturbative calculational approach which yields results that compare very well with exact numerics.Imagine an experiment where a quantum particle inside a box is released at some time in some initial state. A detector is placed at a fixed location inside the box and its clicking signifies arrival of the particle at the detector. What is the time of arrival (TOA) of the particle at the detector ? Within the paradigm of the measurement postulate of quantum mechanics, one can use the idea of projective measurements to define the TOA. We consider a setup where a detector keeps making instantaneous measurements at regular finite time intervals until it detects the particle at time t , which is defined as the TOA. This is a stochastic variable and, for a simple lattice model of a free particle in a one-dimensional box, we find interesting features such as power-law tails in its distribution and in the probability of survival (non-detection). We propose a perturbative calculational approach which yields results that compare very well with exact numerics.

Journal of Physics A Mathematical and TheoreticalFeb 25, 201568 citations

Quantum sensing for particle physics

Steven D. Bass, M. Doser

Nature Reviews PhysicsApr 16, 202456 citations

First-Click Time Measurements

Mafalda Pinto Couto, Lorenzo Maccone, Lorenzo Catani +1 more

There are two distinct perspectives on the quantum time-of-arrival: one can ask for the probability that a particle is found at the detector at a given time, regardless of whether it was previously detected, or for the probability that the particle is detected there for the first time. In this work, we analyze the latter by constructing the time-of-arrival distribution conditioned on the particle not having been detected at earlier times -- the first-click distribution. We work within the Page and Wootters formalism, where time is treated as a quantum observable, and introduce a memory mechanism that records the outcomes of successive detection attempts separated by the detector's finite time resolution. We apply this framework to a single Gaussian wave packet and to a superposition of two overlapping wave packets. We find that conditioning on non-detection redistributes probability toward earlier arrival times, producing narrower and sharper distributions compared with the standard unconditioned case. This effect persists in the presence of quantum interference, though coarser time resolutions broaden the distribution and shift it toward later times.There are two distinct perspectives on the quantum time-of-arrival: one can ask for the probability that a particle is found at the detector at a given time, regardless of whether it was previously detected, or for the probability that the particle is detected there for the first time. In this work, we analyze the latter by constructing the time-of-arrival distribution conditioned on the particle not having been detected at earlier times -- the first-click distribution. We work within the Page and Wootters formalism, where time is treated as a quantum observable, and introduce a memory mechanism that records the outcomes of successive detection attempts separated by the detector's finite time resolution. We apply this framework to a single Gaussian wave packet and to a superposition of two overlapping wave packets. We find that conditioning on non-detection redistributes probability toward earlier arrival times, producing narrower and sharper distributions compared with the standard unconditioned case. This effect persists in the presence of quantum interference, though coarser time resolutions broaden the distribution and shift it toward later times.

quant-pharXiv:2603.28623Mar 31, 20260 citations

Quantum time of arrival distribution in a simple lattice model

Shrabanti Dhar, Subinay Dasgupta, Abhishek Dhar

Imagine an experiment where a quantum particle inside a box is released at some time in some initial state. A detector is placed at a fixed location inside the box and its clicking signifies arrival of the particle at the detector. What is the \emph{time of arrival} (TOA) of the particle at the detector ? Within the paradigm of the measurement postulate of quantum mechanics, one can use the idea of projective measurements to define the TOA. We consider the setup where a detector keeps making instantaneous measurements at regular finite time intervals {\emph{till}} it detects the particle at some time $t$ , which is defined as the TOA. This is a stochastic variable and, for a simple lattice model of a free particle in a one-dimensional box, we find interesting features such as power-law tails in its distribution and in the probability of survival (non-detection). We propose a perturbative calculational approach which yields results that compare very well with exact numerics.Imagine an experiment where a quantum particle inside a box is released at some time in some initial state. A detector is placed at a fixed location inside the box and its clicking signifies arrival of the particle at the detector. What is the \emph{time of arrival} (TOA) of the particle at the detector ? Within the paradigm of the measurement postulate of quantum mechanics, one can use the idea of projective measurements to define the TOA. We consider the setup where a detector keeps making instantaneous measurements at regular finite time intervals {\emph{till}} it detects the particle at some time $t$, which is defined as the TOA. This is a stochastic variable and, for a simple lattice model of a free particle in a one-dimensional box, we find interesting features such as power-law tails in its distribution and in the probability of survival (non-detection). We propose a perturbative calculational approach which yields results that compare very well with exact numerics.

arXiv:1312.5923Dec 20, 20132 citations

Arbitrarily precise arrival time measurements in quantum mechanics

Lawrence Frolov

The quantum Zeno effect is often regarded as an obstruction to precise arrival time measurements in quantum mechanics. Here, an arbitrarily precise arrival time measurement procedure is constructed using a localized detection process and a suitably chosen boundary condition. The arrival time of an incoming particle is recorded in the position of a clock particle that is emitted by the apparatus upon detection. A non-zero probability of arrival is shown to survive even in the limit as exact arrival time measurement precision is achieved. In this limit, it is also found that the interaction between the incoming particle and the detector is described by an absorbing boundary condition. This justifies the claim of Tumulka that absorbing boundary conditions may be used to model idealized detectors capable of registering particles at the instant of their arrival.The quantum Zeno effect is often regarded as an obstruction to precise arrival time measurements in quantum mechanics. Here, an arbitrarily precise arrival time measurement procedure is constructed using a localized detection process and a suitably chosen boundary condition. The arrival time of an incoming particle is recorded in the position of a clock particle that is emitted by the apparatus upon detection. A non-zero probability of arrival is shown to survive even in the limit as exact arrival time measurement precision is achieved. In this limit, it is also found that the interaction between the incoming particle and the detector is described by an absorbing boundary condition. This justifies the claim of Tumulka that absorbing boundary conditions may be used to model idealized detectors capable of registering particles at the instant of their arrival.

quant-pharXiv:2606.01005Jun 2, 20260 citations

t

, which is defined as the TOA. This is a stochastic variable and, for a simple lattice model of a free particle in a one-dimensional box, we find interesting features such as power-law tails in its distribution and in the probability of survival (non-detection). We propose a perturbative calculational approach which yields results that compare very well with exact numerics.