Quantum Channel Marginal Problem

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.

4+11 pages and 1 figure with new results

References in corpus (7)

• N-representability is QMA-complete
• All sets of incompatible measurements give an advantage in quantum state discrimination
• Extendibility limits the performance of quantum processors
• Jordan products of quantum channels and their compatibility
• Quantum Marginal Problem and its Physical Relevance
• Communication, Dynamical Resource Theory, and Thermodynamics
• On state vs. channel quantum extension problems: exact results for UxUxU symmetry

Cited by in corpus (6)

• Unifying different notions of quantum incompatibility into a strict hierarchy of resource theories of communication
• Estimating gate-set properties from random sequences
• Resource Marginal Problems
• Incompatibility of local measurements provide advantage in local quantum state discrimination
• Estimation of correlations and non-separability in quantum channels via unitarity benchmarking
• A geometrical description of the universal $1\to 2$ asymmetric quantum cloning region