Quantum Gibbs states are locally Markovian

Understand

The Markov property entails the conditional independence structure inherent in Gibbs distributions for general classical Hamiltonians, a feature that plays a crucial role in inference, mixing time analysis, and algorithm design.

• However, much less is known about quantum Gibbs states.
• In this work, we show that for any Hamiltonian with a bounded interaction degree, the quantum Gibbs state is locally Markov at arbitrary temperature, meaning there exists a quasi-local recovery map for every local region.
• Notably, this recovery map is obtained by applying a detailed-balanced Lindbladian with jumps acting on the region.