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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UNVERDICTED 2representative citing papers
The Petz recovery map equals the gradient of the log-likelihood in maximum-likelihood tomography, unifying retrodiction and state reconstruction via a shared iterative procedure.
citing papers explorer
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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.
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Connecting Quantum Tomography and Quantum Retrodiction
The Petz recovery map equals the gradient of the log-likelihood in maximum-likelihood tomography, unifying retrodiction and state reconstruction via a shared iterative procedure.