Topic
Matrix and entropy inequalities
15 records: 11 unsolved, 4 solved. Filter the catalog by this topic →
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Quantum Mrs. Gerber lower bound for information combining
Does the quantum Mrs.
Unsolved -
Quantum validity of the Zhang–Yeung inequality
Does the four-party Zhang–Yeung inequality hold for the von Neumann entropies of every finite-dimensional quantum state?
Unsolved -
Quantum erasure-channel upper bound for information combining
Does the quantum erasure-channel upper information-combining bound hold for two independent uniform bits with arbitrary quantum side information?
Unsolved -
Endpoint quantum KKL inequality for Boolean observables
Does the Montanaro–Osborne \(L^2\) quantum KKL inequality hold for every Boolean quantum observable?
Unsolved -
Wigner entropy conjecture
Does every finite-energy single-mode state with a nonnegative Wigner function have Wigner entropy at least \(1+\ln\pi\)?
Solved -
Minimum output entropy additivity for qubit channels
Is minimum output von Neumann entropy additive whenever one channel is a qubit channel?
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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?
Solved -
Entropy photon-number inequality
Does the entropy photon-number inequality hold for every pair of independent finite-energy bosonic inputs?
Unsolved -
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 -
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?
Solved -
Multimode constrained output entropy of a pure-loss channel
Is Guha’s multimode Strong Conjecture 2 true for every correlated input state?
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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