Conditional probabilities in quantum-optical settings

• URL: http://arxiv.org/abs/2607.21100v1
• Date: Thu, 23 Jul 2026 09:30:24 GMT
• Title: Conditional probabilities in quantum-optical settings
• Abstract summary: We show that conditioning on one variable can lead to reduction of uncertainty in the other one.<n>We examine these issues in two basic quantum-optical schemes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We examine conditional probabilities derived from the joint noisy measurement of two complementary observables. We show that conditioning on one variable can lead to reduction of uncertainty in the other one, even completely eliminating uncertainty. We show that the conditional distribution cannot, in general, be represented in Born form using the marginal positive operator valued measure and any physical system state, nor can it be derived from typical rules of state reduction. We examine these issues in two basic quantum-optical schemes. These are double homodyne detection and a qubit measurement.

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