Time-of-arrival probabilities and quantum measurements
arXiv:quant-ph/0509020 · doi:10.1063/1.2399085
Abstract
We study the construction of probability densities for time-of-arrival in quantum mechanics. Our treatment is based upon the facts that (i) time appears in quantum theory as an external parameter to the system, and (ii) propositions about the time-of-arrival appear naturally when one considers histories. The definition of time-of-arrival probabilities is straightforward in stochastic processes. The difficulties that arise in quantum theory are due to the fact that the time parameter of Schrödinger's equation does not naturally define a probability density at the continuum limit, but also because the procedure one follows is sensitive on the interpretation of the reduction procedure. We consider the issue in Copenhagen quantum mechanics and in history-based schemes like consistent histories. The benefit of the latter is that it allows a proper passage to the continuous limit--there are however problems related to the quantum Zeno effect and decoherence. We finally employ the histories-based description to construct Positive-Operator-Valued-Measures (POVMs) for the time-of-arrival, which are valid for a general Hamiltonian. These POVMs typically depend on the resolution of the measurement device; for a free particle, however, this dependence cancels in the physically relevant regime and the POVM coincides with that of Kijowski.
40 pages, 1 fig.--expanded argumentation, version to appear in JMP
References in corpus (4)
Cited by in corpus (42)
- Detection of a quantum particle on a lattice under repeated projective measurements
- Arrival Times, Complex Potentials and Decoherent Histories
- Quasiprobabilistic Interpretation of Weak measurements in Mesoscopic Junctions
- Time-of-arrival probabilities for general particle detectors
- Disclosing hidden information in the quantum Zeno effect: Pulsed measurement of the quantum time of arrival
- Intrinsic and Fundamental Decoherence: Issues and Problems
- Exotic Bohmian arrival times of spin-1/2 particles I-An analytical treatment
- Formulation of Time-Resolved Counting Statistics Based on a Positive-Operator-Valued Measure
- Dark states of quantum search cause imperfect detection
- Quantum Backflow States from Eigenstates of the Regularized Current Operator
- Spread complexity for measurement-induced non-unitary dynamics and Zeno effect
- Quantum Field Theory based Quantum Information: Measurements and Correlations
- Quantum Arrival Time Formula from Decoherent Histories
- Time of arrival and localization of relativistic particles
- Classical Vs Quantum Probability in Sequential Measurements
- Times of Arrival and Gauge Invariance
- Pitfalls of Path Integrals: Amplitudes for Spacetime Regions and the Quantum Zeno Effect
- The spectral dimension controls the decay of the quantum first detection probability
- Coherences of accelerated detectors and the local character of the Unruh effect
- Time-of-arrival correlations
- Quantum temporal probabilities in tunneling systems
- Time-of-arrival probabilities and quantum measurements: II Application to tunneling times
- A self-adjoint arrival time operator inspired by measurement models
- Time-of-arrival probabilities and quantum measurements: III Decay of unstable states
- Decays of unstable quantum systems
- Quantum Information in Relativity: the Challenge of QFT Measurements
- The time distribution of quantum events
- Spacetime Coarse Grainings in the Decoherent Histories Approach to Quantum Theory
- Characterizing Multiple Solutions to the Time-Energy Canonical Commutation Relation via Quantum Dynamics
- Characterizing Multiple Solutions to the Time - Energy Canonical Commutation Relation via Internal Symmetries
- Real-time particle-detection probabilities in accelerated macroscopic detectors
- Path of a tunneling particle
- Towards a Field-Theory based Relativistic Quantum Information
- Pointer-based model for state reduction in momentum space
- Multi-Time Measurements in Hawking Radiation: Information at Higher-Order Correlations
- Nonideal Quantum Measurement Effects on the Switching Currents Distribution of Josephson Junctions
- Amplitudes for Spacetime Regions and the Quantum Zeno Effect: Pitfalls of Standard Path Integral Constructions
- Long quantum transition times due to unstable semiclassical dynamics
- Does the Heisenberg uncertainty principle apply along the time dimension?
- Accurate Switching Currents Measurements in Quantum Washboard Potential
- Qubit-based momentum measurement of a particle
- Contrary Inferences for Classical Histories within the Consistent Histories Formulation of Quantum Theory