Quantum probabilities for time-extended measurements

Abstract

We study the probability assignment for the outcomes of time-extended measurements. We construct the class-operator that incorporates the information about a generic time-smeared quantity. These class-operators are employed for the construction of Positive-Operator-Valued-Measures for the time-averaged quantities. The scheme highlights the distinction between velocity and momentum in quantum theory. Propositions about velocity and momentum are represented by different class-operators, hence they define different probability measures. We provide some examples, we study the classical limit and we construct probabilities for generalized time-extended phase space variables.

17 pages, latex

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Cited by in corpus (8)

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• Pitfalls of Path Integrals: Amplitudes for Spacetime Regions and the Quantum Zeno Effect
• Time-of-arrival correlations
• Quantum temporal probabilities in tunneling systems
• Time-of-arrival probabilities and quantum measurements: II Application to tunneling times
• Amplitudes for Spacetime Regions and the Quantum Zeno Effect: Pitfalls of Standard Path Integral Constructions
• Phase Space Representations and Perturbation Theory for Continuous-time Histories