Quantum Conditional Mutual Information and Approximate Markov Chains

By Omar Fawzi, Renato Renner. Communications in Mathematical Physics, 2014

332 citations recorded by the source corpus.

A state on a tripartite quantum system A⊗B⊗C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A \otimes B \otimes C}$$\end{document} forms a Markov chain if it can be reconstructed from its marginal on A⊗B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A \otimes B}$$\end{document} by a quantum operation from B to B⊗C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B \otimes C}$$\end{document}. We show that the quantum conditional mutual information I(A : C|B) of an arbitrary state is an upper bound on its distance to the closest reconstructed state. It thus quantifies how well the Markov chain property is approximated.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/613d21e59b27a1f0ee8388930d10e14d34e5c618

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

  1. Ahmed Almheiri
  2. D. Marolf
  3. Netta Engelhardt
  4. Henry Maxfield

In Atomic and Molecular Physics, and Optics

  1. Ahmed Almheiri
  2. Henry Maxfield
  3. D. Marolf
  4. S. Raju
  5. Netta Engelhardt
  6. J. Maldacena
  7. Geoffrey Penington
  8. D. Stanford

Citations in the corpus