Given a set of local dynamics, are they compatible with a global dynamics? We systematically formulate these questions as quantum channel marginal problems, which can be understood as a dynamical generalization of the marginal problems for quantum states. After defining the notion of compatibility between global and local dynamics, we provide a necessary and sufficient condition for it, showing that it takes the form of a semidefinite program. Using this formulation, we construct channel incompatibility witnesses and show that a set of local channels are incompatible if and only if they demonstrate an advantage in a state-discrimination task.

Chung-Yun Hsieh received the B.S./M.S. degrees from National Tsing Hua University, Hsinchu, Taiwan, in 2013 and 2016, respectively, with B.S. in physics and mathematics (in the interdisciplinary program of science) and M.S. in physics. He is currently a Ph.D. student with ICFO – The Institute of Photonic Sciences (Institut de Ciències Fotòniques), Barcelona, Spain. His research interests include several topics in theoretical quantum information science, such as quantum resource theory, quantum thermodynamics, and quantum foundation.