Recoverability from direct quantum correlations. (15th April 2020)

• Record Type: Journal Article
• Authors: Di Giorgio, S; Mateus, P; Mera, B
• Is Part Of: Journal of physics. Volume 53:Number 18(2020)
• Publication Date: 2020-04-15
• Subjects: quantum Markov chains -- maximum von Neumann entropy -- bipartite correlations -- quantum trees; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ab7a52
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: 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 .