Quantum channel marginal problem

Chung Yun Hsieh*, Matteo Lostaglio, Antonio Acín

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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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.

Original languageEnglish
Article numberA194
Number of pages14
JournalPhysical Review Research
Volume4
Issue number1
DOIs
Publication statusPublished - 2022

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