Quantum Channel Marginal Problem
- URL: http://arxiv.org/abs/2102.10926v4
- Date: Mon, 31 Jan 2022 10:13:17 GMT
- Title: Quantum Channel Marginal Problem
- Authors: Chung-Yun Hsieh, Matteo Lostaglio, and Antonio Ac\'in
- Abstract summary: 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.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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