1D translation-invariant Gibbs states at positive temperature exhibit superexponential decay of Belavkin-Staszewski conditional mutual information, enabling efficient learning from local measurements and tensor network approximations.
Monotonicity of quantum relative entropy revisited
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abstract
Monotonicity under coarse-graining is a crucial property of the quantum relative entropy. The aim of this paper is to investigate the condition of equality in the monotonicity theorem and in its consequences such as the strong sub-additivity of the von Neumann entropy, the Golden-Thompson trace inequality and the monotonicity of the Holevo quantity.The relation to quantum Markovian states is briefly indicated.
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quant-ph 1years
2024 1verdicts
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Conditional Independence of 1D Gibbs States with Applications to Efficient Learning
1D translation-invariant Gibbs states at positive temperature exhibit superexponential decay of Belavkin-Staszewski conditional mutual information, enabling efficient learning from local measurements and tensor network approximations.