Topic
Additivity and regularization
11 records: 9 unsolved, 2 solved. Filter the catalog by this topic →
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Additivity of the relative entropy of entanglement
Does the relative entropy of entanglement of every bipartite state equal its regularization, or is regularization genuinely necessary?
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Additivity of the entanglement of purification
Is the entanglement of purification additive on tensor products?
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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?
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Private capacity of the qubit depolarizing channel
What is the private classical capacity \(P(\Lambda_p)\) of the qubit depolarizing channel, defined for a mixing parameter \(p\in[0,1]\) by
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Closed-form nonadditivity of the Holevo capacity and entanglement of formation
Construct a simple closed-form or practically computable counterexample to additivity of the Holevo capacity or the entanglement of formation, together with a rigorous certificate of a strict violation.
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Closed-form exact PPT distillable entanglement
What computable expression, if any, equals the regularized exact PPT distillable entanglement of a bipartite state?
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Universal finite truncation of quantum and private capacities
Do there exist channel-independent finite integers \(m_Q\) and \(m_P\) that determine, respectively, the quantum capacity and the private classical capacity of every finite-dimensional quantum channel?
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Structural criterion for classical–entanglement trade-off advantage
Characterize the finite-dimensional quantum channels for which joint classical–entanglement coding strictly outperforms time sharing between unassisted and unlimited-entanglement classical communication.
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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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Collective cost of tensor-power state preparation
Determine the asymptotic weighted circuit cost of preparing tensor powers of a known pure state, and characterize when collective preparation is cheaper per copy than independent preparation.
Unsolved