A lower bound of quantum conditional mutual information

Abstract

In this paper, a lower bound of quantum conditional mutual information is obtained by employing the Peierls-Bogoliubov inequality and Golden Thompson inequality. Comparison with the bounds obtained by other researchers indicates that our result is independent of any measurements. It may give some new insights over squashed entanglement and perturbations of Markov chain states.

11 pages, LaTeX, published version. The missed second author is also added

References in corpus (5)

• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Quantum Graphical Models and Belief Propagation
• Remainder Terms for Some Quantum Entropy Inequalities
• The Golden-Thompson inequality --- historical aspects and random matrix applications
• Determining the structure of real-space entanglement spectrum from approximate conditional independence

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• Renyi generalizations of the conditional quantum mutual information
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• Quantum Markov chains, sufficiency of quantum channels, and Renyi information measures
• Operational meaning of quantum measures of recovery
• Fidelity between a bipartite state and another one undergoing local unitary dynamics
• A strengthened monotonicity inequality of quantum relative entropy: A unifying approach via Rényi relative entropy
• On some entropy inequalities
• Entanglement and other quantum correlations of a single qudit state as a resource for quantum technologies
• Estimating Rényi's $\alpha$-Cross-Entropies in a Matrix-Based Way