Entanglement preserving local thermalization

We investigate whether entanglement can survive the thermalization of subsystems. We present two equivalent formulations of this problem: (1) Can two isolated agents, accessing only pre-shared randomness, locally thermalize arbitrary input states while maintaining some entanglement? (2) Can thermalization with local heat baths, which may be classically correlated but do not exchange information, locally thermalize arbitrary input states while maintaining some entanglement? We answer these questions in the positive at every nonzero temperature and provide bounds on the amount of preserved entanglement. We provide explicit protocols and discuss their thermodynamic interpretation: we suggest that the underlying mechanism is a speed-up of the subsystem thermalization process. We also present extensions to multipartite systems. Our findings show that entanglement can survive locally performed thermalization processes accessing only classical correlations as a resource. They also suggest a broader study of the channel's ability to preserve resources and of the compatibility between global and local dynamics.Comment: 6+7 pages, 1 figure, closed to the published versio

Quantum Channel Marginal Problem

Given a set of local dynamics, are they compatible with a global dynamics? We systematically formulate these questions as quantum channel marginal problems, which can be understood as a dynamical generalization of the marginal problems for quantum states. These problems include as special cases channel broadcasting, channel extendibility, and measurement compatibility and are strongly connected to the generalization of the no-signaling conditions to quantized inputs and outputs. 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 and show that a set of local channels are incompatible if and only if they demonstrate an advantage in a state-discrimination task.Comment: 4+10 pages and 1 figure with a generalized framework, stronger results, and improved writin