Saturation of repeated quantum measurements

Abstract

We study sequential measurement scenarios where the system is repeatedly subjected to the same measurement process. We first provide examples of such repeated measurements where further repetitions of the measurement do not increase our knowledge on the system after some finite number of measurement steps. We also prove, however, that repeating the Lüders measurement of an unsharp two-outcome observable never saturates in this sense, and we characterize the observable measured in the limit of infinitely many repetitions. Our result implies that a repeated measurement can be used to correct the inherent noise of an unsharp observable.

14 pages, one figure; v2 minor changes, different title

References in corpus (5)

• Progressive field-state collapse and quantum non-demolition photon counting
• Clean Positive Operator Valued Measures
• Sharp and fuzzy observables on effect algebras
• Sequential measurements of conjugate observables
• A Kolmogorov Extension Theorem for POVMs

Cited by in corpus (8)

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• Theory of Metastability in Discrete-Time Open Quantum Dynamics
• Quantum state tomography via sequential uses of the same informationally incomplete measuring apparatus
• Quantum State Discrimination via Repeated Measurements and the Rule of Three