Quantum channel marginal problem
Chung Yun Hsieh (Barcelona Institute of Science and Technology (BIST))
Matteo Lostaglio (Barcelona Institute of Science and Technology (BIST), TU Delft - QCD/Terhal Group, TU Delft - Architecture and the Built Environment, Universiteit van Amsterdam, TU Delft - QuTech Advanced Research Centre)
Antonio Acín (Catalan Institution for Research and Advanced Studies (ICREA), Barcelona Institute of Science and Technology (BIST))
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
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. Using this formulation, we construct channel incompatibility witnesses, discuss their operational interpretation in terms of an advantage for a state-discrimination task, prove a gap between classical and quantum dynamical marginal problems, and show that the latter is irreducible to state marginal problems.
help_outline