Consequences of a dynamical no-signaling condition for classical-quantum interactions

• URL: http://arxiv.org/abs/2608.07245v1
• Date: Fri, 07 Aug 2026 14:03:03 GMT
• Title: Consequences of a dynamical no-signaling condition for classical-quantum interactions
• Abstract summary: We propose to describe hybrid systems starting from a set of natural axioms for measurement probabilities.<n>For two independent systems, the outcome probabilities of a measurement made on one of them are not affected by a measurement performed earlier on the other.<n>The proposed condition is equivalent to the convex-linearity of the probability measure transformations describing finite-time evolutions.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Hybrid classical-quantum approaches are instrumental in numerous fields, from condensed matter physics to quantum information science. We recently proposed to describe hybrid systems starting from a set of natural axioms for measurement probabilities without adding any underlying mathematical structure. The so defined probability measures fulfill a no-signaling condition that ensures that instantaneous communication is impossible. We formulate here a dynamical generalization of this condition. It means that, for two independent systems, the outcome probabilities of a measurement made on one of them are not affected by a measurement performed earlier on the other. Analogous requirements are satisfied for usual classical and quantum bipartite systems and violating them would make faster-than-light signaling possible. The dynamical no-signaling condition has important consequences for classical-quantum interactions that depend on the hybrid approach used. For no-signaling hybrid dynamics with classical trajectories, the classical degrees of freedom can influence the quantum ones but the latter cannot react on the former. If pure states of quantum systems remain pure then the dynamical no-signaling condition implies the absence of classical reaction. When all hybrid states are allowed, there are no genuine classical-quantum interactions for no-signaling hybrid dynamics that do not generate correlations between the classical and the quantum degrees of freedom. In all these cases, the proposed condition is equivalent to the convex-linearity of the probability measure transformations describing finite-time evolutions.

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