2016/09/27 by Isaac H. Kim, Kim, Isaac H.
Computer Science · Mathematics · Physics and Astronomy · #Bayesian Modeling and Causal Inference #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.1609.08579
openalex publication_date 2016/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a class of so called Markovian marginals, which gives a natural framework for constructing solutions to the quantum marginal problem. We consider a set of marginals that possess a certain internal quantum Markov chain structure. If they are equipped with such a structure and are locally consistent on their overlapping supports, there exists a global state that is consistent with all the marginals. The proof is constructive, and relies on a reduction of the marginal problem to a certain combinatorial problem. By employing an entanglement entropy scaling law, we give a physical argument that the requisite structure exists in any states with finite correlation lengths. This includes topologically ordered states as well as finite temperature Gibbs states.