TY - JOUR
T1 - Quantum channel marginal problem
AU - Hsieh, Chung Yun
AU - Lostaglio, Matteo
AU - Acín, Antonio
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85129101852&partnerID=8YFLogxK
U2 - 10.1103/PhysRevResearch.4.013249
DO - 10.1103/PhysRevResearch.4.013249
M3 - Article
AN - SCOPUS:85129101852
SN - 2643-1564
VL - 4
JO - Physical Review Research
JF - Physical Review Research
IS - 1
M1 - A194
ER -