Quantum Channel Marginal Problem

Understand

Given a set of local dynamics, are they compatible with a global dynamics? We systematically formulate these questions as quantum channel marginal problems.

• These problems are strongly connected to the generalization of the no-signaling conditions to quantized inputs and outputs and can be understood as a general toolkit to study notions of quantum incompatibility.
• In fact, they include as special cases channel broadcasting, channel extendibility, measurement compatibility, and state marginal problems.
• After defining the notion of compatibility between global and local dynamics, we provide a solution to the channel marginal problem that takes the form of a semidefinite program.