Continuous Observation of Quantum Systems

• URL: http://arxiv.org/abs/2607.01158v2
• Date: Fri, 03 Jul 2026 17:34:47 GMT
• Title: Continuous Observation of Quantum Systems
• Abstract summary: In the 1980's Alexander Holevo proved a classification theorem for continuous quantum measurement processes.<n>Here we give an alternative, more probabilistic proof: we use weak convergence of measures and employ Levy's Continuity Theorem.<n>We clarify the boundedness conditions in Holevo's theorem, and supply a simple example from quantum optics.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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