Conditional mutual information and self-commutator

Abstract

A simpler approach to the characterization of vanishing conditional mutual information is presented. Some remarks are given as well. More specifically, relating the conditional mutual information to a commutator is a very promising approach towards the approximate version of SSA. That is, it is conjectured that small conditional mutual information implies small perturbation of quantum Markov chain.

LaTex, 9 pages. Minor modifications are made. Any comments are welcome!

References in corpus (4)

• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Faithful Squashed Entanglement
• Quantum f-divergences and error correction
• Quantum Graphical Models and Belief Propagation

Cited by in corpus (12)

• Quantum conditional mutual information and approximate Markov chains
• Quantum Conditional Mutual Information, Reconstructed States, and State Redistribution
• Squashed entanglement, k-extendibility, quantum Markov chains, and recovery maps
• Universal recovery map for approximate Markov chains
• The Fidelity of Recovery is Multiplicative
• Conditional Mutual Information of Bipartite Unitaries and Scrambling
• Measures of quantum correlations in infinite-dimensional systems
• Local measures of entanglement in black holes and CFTs
• Approximate quantum Markov chains
• A lower bound of quantum conditional mutual information
• On lower semicontinuity of the quantum conditional mutual information and its corollaries
• A strengthened monotonicity inequality of quantum relative entropy: A unifying approach via Rényi relative entropy