Topic
Matrix and entropy inequalities
8 records: 6 unsolved, 2 solved. Filter the catalog by this topic →
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Smallest output dimension violating minimum output entropy additivity
What is the smallest output dimension in which the minimum output von Neumann entropy of quantum channels fails to be additive?
Unsolved -
Multimode constrained output entropy of a pure-loss channel
Is Guha’s multimode Strong Conjecture 2 true for every correlated input state?
Unsolved -
Ordinary-Petz recovery bound for conditional mutual information
Does the ordinary, unrotated Petz map universally recover a tripartite state with fidelity controlled by its conditional mutual information?
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Ordinary-Petz fidelity remainder for relative-entropy data processing
Does the ordinary Petz recovery map give a universal fidelity remainder for monotonicity of quantum relative entropy?
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Umegaki relative entropy of local recovery
Does the conditional mutual information of every finite-dimensional tripartite state dominate its Umegaki relative entropy of local recovery?
Solved -
Multiplicativity for polarized Werner–Holevo channels
For every integer \(d\geq3\), every \(x\in(0,1)\), and every \(1<p<2\), is the maximal output Schatten \(p\)-norm of the polarized Werner–Holevo channel multiplicative on two identical copies?
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Delayed-onset additivity violation for minimum output Rényi entropy
Does there exist a finite-dimensional quantum channel whose minimum output Rényi entropy is additive for every tensor power below some order and first becomes strictly subadditive at that order?
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Trace-exponential lower bound for matrix-word averages
Is the normalized trace average of all words in two positive-definite matrices always bounded below by the corresponding trace exponential?
Unsolved