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We derive general conditions for the compatibility of channels in generalprobabilistic theory. We introduce formalism that allows us to easily formulatesteering by channels and Bell nonlocality of channels as generalizations of thewell-known concepts of steering by measurements and Bell nonlocality ofmeasurements. The generalization does not follow the standard line of thinkingstemming from the Einstein-Podolsky-Rosen paradox, but introduces steering andBell nonlocality as entanglement-assisted incompatibility tests. We show thatall of the proposed definitions are, in the special case of measurements, thesame as the standard definitions, but not all of the known results formeasurements generalize to channels. For example, we show that for quantumchannels, steering is not a necessary condition for Bell nonlocality. Wefurther investigate the introduced conditions and concepts in the special caseof quantum theory and we provide many examples to demonstrate these conceptsand their implications.

Conditions for the compatibility of channels in general probabilistic theory and their connection to steering and Bell nonlocality