Quantum channel marginal problem

Given a set of local dynamics, are they compatible with global dynamics? We systematically formulate these questions as quantum channel marginal problems. These problems strongly connected to the generalization no-signaling conditions quantized inputs and outputs can be understood general toolkit study notions incompatibility. In fact, include special cases broadcasting, extendibility, measurement compatibility, state After defining notion compatibility between we provide solution problem that takes form semidefinite program. Using this formulation, construct incompatibility witnesses, discuss their operational interpretation in terms an advantage for state-discrimination task, prove gap classical dynamical show latter is irreducible