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arXiv · 2607.01158

Continuous Observation of Quantum Systems

Hans Maassen
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Abstract

In a series of papers in the 1980's Alexander Holevo proved a classification theorem for continuous quantum measurement processes, or, as they would today be called, stationary quantum trajectories in continuous time. His main tools were functional analytic in character: starting from a Bochner-type inequality he employed dilation techniques for positive definite kernels. Here we give an alternative, more probabilistic proof: we use weak convergence of measures and employ Levy's Continuity Theorem. We clarify the boundedness conditions in Holevo's theorem, and supply a simple example from quantum optics.

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Hans Maassen. 2026-07-01. Continuous Observation of Quantum Systems. https://doi.org/10.1142/s0219749924020015

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