Recoverability from direct quantum correlations

S. Di Giorgio, P. Mateus, B. Mera

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We address the problem of compressing density operators defined on a finite dimensional Hilbert space which assumes a tensor product decomposition. In particular, we look for an efficient procedure for learning the most likely density operator, according to 'Jaynes' principle, given a chosen set of partial information obtained from the unknown quantum system we wish to describe. For complexity reasons, we restrict our analysis to tree-structured sets of bipartite marginals. We focus on the tripartite scenario, where we solve the problem for the couples of measured marginals which are compatible with a quantum Markov chain, providing then an algebraic necessary and sufficient condition for the compatibility to be verified. We introduce the generalization of the procedure to the n-partite scenario, giving some preliminary results. In particular, we prove that if the pairwise Markov condition holds between the subparts then the choice of the best set of tree-structured bipartite marginals can be performed efficiently. Moreover, we provide a new characterization of quantum Markov chains in terms of quantum Bayesian updating processes.

Original languageEnglish
Article number185301
JournalJournal of Physics A: Mathematical and Theoretical
Issue number18
Publication statusPublished - 2020 May 11
Externally publishedYes


  • bipartite correlations
  • maximum von Neumann entropy
  • Quantum Markov chains
  • quantum trees

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)


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