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

• URL: http://arxiv.org/abs/2207.09140v3
• Date: Mon, 5 Jun 2023 08:54:46 GMT
• Title: Passive quantum measurement: Arrival time, quantum Zeno effect and gambler's fallacy
• Authors: Tajron Juri\'c, Hrvoje Nikoli\'c
• Abstract summary: We find that quantum projective measurement can be passive in a way which is impossible in finite dimensional Hilbert spaces. The avoidance of quantum Zeno effect can also be understood as avoidance of a quantum version of gambler's fallacy.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 departs rather than arrives.

Related papers

• Probing the nonclassical dynamics of a quantum particle in a gravitational field [0.0]
  In quantum mechanics, the time evolution of particles is given by the Schr"odinger equation. We propose to measure the effects of an asymmetric mass configuration on a quantum particle in an interferometer.
  arXiv  Detail & Related papers  (2025-02-05T00:15:01Z)
• Is the Born rule a result of measurement noise? [0.0]
  The Born rule asserts the distribution of eigenstates observed in unbiased quantum measurements, but the reason it holds remains elusive. This manuscript discusses how the Born rule might be explained by Schrodinger equation dynamics.
  arXiv  Detail & Related papers  (2024-07-03T14:20:11Z)
• A Method Using Photon Collapse and Entanglement to Transmit Information [13.438312709072457]
  We find that measurements cause quantum wave functions to collapse. By studying the overlooked phenomena of quantum wave function collapse, we find that quantum eigenstate sets may be artificially controlled. We propose an innovative method for direct information transmission utilizing photon wave function collapse and entanglement.
  arXiv  Detail & Related papers  (2024-06-27T13:22:21Z)
• Effect of measurements on quantum speed limit [0.0]
  We show that under continuous measurement, the speed of transportation of a quantum system tends to zero. For small time scale, there is an enhancement of quantum speed even if the measurement strength is finite. Our findings can have applications in quantum computing and quantum control where dynamics is governed by both unitary and measurement processes.
  arXiv  Detail & Related papers  (2024-06-13T11:14:22Z)
• A computational test of quantum contextuality, and even simpler proofs of quantumness [43.25018099464869]
  We show that an arbitrary contextuality game can be compiled into an operational "test of contextuality" involving a single quantum device. Our work can be seen as using cryptography to enforce spatial separation within subsystems of a single quantum device.
  arXiv  Detail & Related papers  (2024-05-10T19:30:23Z)
• Randomly Monitored Quantum Codes [8.557392136621894]
  Recent studies have shown that quantum measurement itself can induce novel quantum phenomena. One example is a monitored random circuit, which can generate long-range entanglement faster than a random unitary circuit. In particular, we demonstrate that for a large class of quantum error-correcitng codes, it is impossible to destroy the encoded information through random single-qubit Pauli measurements.
  arXiv  Detail & Related papers  (2024-01-31T19:53:06Z)
• Quantum Instability [30.674987397533997]
  We show how a time-independent, finite-dimensional quantum system can give rise to a linear instability corresponding to that in the classical system. An unstable quantum system has a richer spectrum and a much longer recurrence time than a stable quantum system.
  arXiv  Detail & Related papers  (2022-08-05T19:53:46Z)
• Experimental study of quantum uncertainty from lack of information [3.901856932788151]
  The uncertainty in the classical domain comes from the lack of information about the exact state of the system. In this paper we investigate the issue experimentally by implementing the corresponding two-dimensional and three-dimensional guessing games. Our results confirm that within the guessing-game framework, the quantum uncertainty to a large extent relies on the fact that quantum information determining the key properties of the game is stored in the degrees of freedom that remain inaccessible to the guessing party.
  arXiv  Detail & Related papers  (2021-05-19T09:15:27Z)
• Quantum indistinguishability through exchangeable desirable gambles [69.62715388742298]
  Two particles are identical if all their intrinsic properties, such as spin and charge, are the same. Quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. We show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.
  arXiv  Detail & Related papers  (2021-05-10T13:11:59Z)
• Energy Non-Conservation in Quantum Mechanics [0.0]
  We study the conservation of energy, or lack thereof, when measurements are performed in quantum mechanics. In Everettian quantum theory, while the expectation value of the Hamiltonian is conserved for the wave function of the universe, it is not constant within individual worlds.
  arXiv  Detail & Related papers  (2021-01-26T19:47:20Z)
• Quantum Zeno effect appears in stages [64.41511459132334]
  In the quantum Zeno effect, quantum measurements can block the coherent oscillation of a two level system by freezing its state to one of the measurement eigenstates. We show that the onset of the Zeno regime is marked by a $textitcascade of transitions$ in the system dynamics as the measurement strength is increased.
  arXiv  Detail & Related papers  (2020-03-23T18:17:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.