Conditional Mutual Information and Commutator

2012/12/31 by Lin Zhang · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Characterization (materials science) #Commutator #Conditional mutual information #Markov chain #Mutual information #Pointwise mutual information #Quantum #Quantum Computing Algorithms and Architecture #Statistical Mechanics and Entropy #math-ph #math.FA #math.MP #math.OA #quant-ph

paper · pdf · doi:10.1007/s10773-013-1505-7

published as Int. J. Theor. Phys. 52(6): 2112-2117 (2013) · LaTex, 9 pages. Minor modifications are made. Any comments are welcome!

arxiv created 2013/01/22 · openalex publication_date 2013/02/07 · arxiv updated 2013/05/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

Citations

• MONOTONICITY OF QUANTUM RELATIVE ENTROPY REVISITED
• SUFFICIENCY OF CHANNELS OVER VON NEUMANN ALGEBRAS
• Structure of States Which Satisfy Strong Subadditivity of Quantum Entropy with Equality

Cited by

• A lower bound of quantum conditional mutual information