A dynamical no-signaling condition for classical-quantum systems is equivalent to convex-linearity of evolution and forbids back-reaction on classical trajectories, back-reaction on pure quantum states, and interaction without correlation.
Bohr,Atomic Physics and Human Knowledge(Wiley, New York, 1958)
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Consequences of a dynamical no-signaling condition for classical-quantum interactions
A dynamical no-signaling condition for classical-quantum systems is equivalent to convex-linearity of evolution and forbids back-reaction on classical trajectories, back-reaction on pure quantum states, and interaction without correlation.