Topic

Additivity and regularization

17 records: 14 unsolved, 3 solved. Filter the catalog by this topic →

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
Unsolved
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?
Solved
Additivity of the entanglement of purification
Is the entanglement of purification additive on tensor products?
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
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.
Unsolved
Closed-form exact PPT distillable entanglement
What computable expression, if any, equals the regularized exact PPT distillable entanglement of a bipartite state?
Unsolved
Optimal asymptotic distillation yield of dephased T states
What is the optimal catalyst-free asymptotic \(T\)-state yield of a dephased single-qubit \(T\) state?
Unsolved
Additivity of entanglement of formation for two-mode Gaussian states
Is unrestricted entanglement of formation additive on tensor powers of every finite-energy two-mode Gaussian state?
Unsolved
Minimum output entropy additivity for qubit channels
Is minimum output von Neumann entropy additive whenever one channel is a qubit channel?
Unsolved
Low-energy Holevo additivity for a squeezed thermal attenuator
Is energy-constrained Holevo information additive for a squeezed thermal attenuator below its water-filling threshold?
Unsolved
Quantum capacity of higher-dimensional depolarizing channels
What is the unassisted quantum capacity of a depolarizing channel in every finite dimension \(d\geq3\)?
Unsolved
Universal strong converse for the classical capacity
Does every finite-dimensional quantum channel satisfy the strong converse property at its unassisted classical capacity, or does some channel admit a sequence of codes above capacity whose average success probability stays bounded away from zero?
Solved
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?
Solved
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.
Unsolved
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?
Unsolved
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?
Unsolved
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