When does a particle arrive?

Simone, Roncallo,; Sacha, Krzysztof; Maccone, Lorenzo

doi:10.48550/arxiv.2205.02219

Cited by 3 publications

(3 citation statements)

References 34 publications

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“…This problem has a long history, see e.g. [43][44][45][46] for reviews. Here we shall first propose the solution of the problem using only elementary physics, after which we shall show that the same result is obtained with our theory of passive quantum measurements.…”

Section: Arrival Time Distributionmentioning

confidence: 99%

Passive Quantum Measurement: Arrival Time, Quantum Zeno Effect and Gambler's Fallacy

Jurić

Nikolić

2023

Fortschritte der Physik

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Classical measurements are passive, in the sense that they do not affect the physical properties of the measured system. Normally, quantum measurements are not passive in that sense. In the infinite dimensional Hilbert space, however, it is found that quantum projective measurement can be passive in a way which is impossible in finite dimensional Hilbert spaces. Specifically, it is found that expectation value of a hermitian Hamiltonian can have an imaginary part in the infinite dimensional Hilbert space and that such an imaginary part implies a possibility to avoid quantum Zeno effect, which can physically be realized in quantum arrival experiments. The avoidance of quantum Zeno effect can also be understood as avoidance of a quantum version of gambler's fallacy, leading to the notion of passive quantum measurement that updates information about the physical system without affecting its physical properties. The arrival time probability distribution of a particle is found to be given by the flux of the probability current. Possible negative fluxes correspond to regimes at which there is no arrival at all, physically understood as regimes at which the particle departs rather than arrives.

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Section: Arrival Time Distributionmentioning

confidence: 99%

Passive Quantum Measurement: Arrival Time, Quantum Zeno Effect and Gambler's Fallacy

Jurić

Nikolić

2023

Fortschritte der Physik

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show abstract

“…This problem has a long history, see e.g. [41][42][43][44] for reviews. Here we shall first propose the solution of the problem using only elementary physics, after which we shall show that the same result is obtained with our theory of passive quantum measurements.…”

Section: Arrival Time Distributionmentioning

confidence: 99%

Passive quantum measurement: Arrival time, quantum Zeno effect and gambler's fallacy

Jurić¹,

Nikolić²

2022

Preprint

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Classical measurements are passive, in the sense that they do not affect the physical properties of the measured system. Normally, quantum measurements are not passive in that sense. In the infinite dimensional Hilbert space, however, we find that quantum projective measurement can be passive in a way which is impossible in finite dimensional Hilbert spaces. Specifically, we find that expectation value of a hermitian Hamiltonian can have an imaginary part in the infinite dimensional Hilbert space and that such an imaginary part implies a possibility to avoid quantum Zeno effect, which can physically be realized in quantum arrival experiments. The avoidance of quantum Zeno effect can also be understood as avoidance of a quantum version of gambler's fallacy, leading to the notion of passive quantum measurement that updates information about the physical system without affecting its physical properties. The arrival time probability distribution of a particle is found to be given by the flux of the probability current. Possible negative fluxes correspond to regimes at which there is no arrival at all, physically understood as regimes at which the particle departures rather than arrives.

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“…Studies on 'Time' in quantum theory have been debated from its inception [5]. The various notions like Mean First passage time, first arrival time distribution, first detected time, etc has been debated extensively [6,7,8,9,10,11,12,13,14,15,16]. Our work is concerned with the first detected time of the particles under the quantum evolution as explored in the Ref [17,18,19,20,21].…”

Section: Introductionmentioning

confidence: 99%

Non-Hermitian description of sharp quantum resetting

Modak¹,

Aravinda²

2023

Preprint

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We study a non-interacting quantum particle, moving on a one-dimensional, which is subjected to repetitive measurements. We investigate the consequence when such motion is interrupted and restarted from the same initial configuration, known as the quantum resetting problem. We show that such systems can be described by the time evolution under certain timedependent non-Hermitian Hamiltonians. We construct two such Hamiltonians and compare the results with the exact dynamics. Using this effective non-Hermitian description we evaluate the timescale of the survival probability as well as the optimal resetting time for the system.

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When does a particle arrive?

Cited by 3 publications

References 34 publications

Passive Quantum Measurement: Arrival Time, Quantum Zeno Effect and Gambler's Fallacy

Passive Quantum Measurement: Arrival Time, Quantum Zeno Effect and Gambler's Fallacy

Passive quantum measurement: Arrival time, quantum Zeno effect and gambler's fallacy

Non-Hermitian description of sharp quantum resetting

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