Entanglement measures

Does the semidefinite hierarchy for exact PPT entanglement cost collapse at its second level for every finite-dimensional bipartite density operator \(\rho_{AB}\)?

• Quantum Resource Theory
• Entanglement cost
• PPT-preserving operations
• Entanglement measures

What is the squashed entanglement \(E_{\mathrm{sq}}(\Lambda_p)\) of the qubit depolarizing channel, defined for a mixing parameter \(p\in[0,1]\) by

• Quantum Resource Theory
• Quantum Communication
• Entanglement measures
• Quantum capacity
• Private capacity

Is the entanglement of purification additive on tensor products?

• Quantum Resource Theory
• Entanglement measures
• Additivity and regularization

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.

• Quantum Communication
• Quantum Resource Theory
• Classical capacity
• Additivity and regularization
• Entanglement measures

Does Gaussian entanglement of formation equal unrestricted entanglement of formation for every non-bisymmetric multimode Gaussian state?

• Quantum Resource Theory
• Gaussian quantum information
• Entanglement measures

Is there a closed-form formula for the squashed entanglement \(E_{\mathrm{sq}}\) of an arbitrary two-qubit Bell-diagonal state, or a certified approach to determining it numerically?

• Quantum Resource Theory
• Entanglement measures
• Bell-diagonal states

For every local dimension \(d\geq3\), determine the entanglement of formation of an arbitrary Weyl–Bell-diagonal state.

• Quantum Resource Theory
• Entanglement measures
• Bell-diagonal states

Find a closed formula for the relative entropy of entanglement of every two-qubit density operator \(\rho\), including an explicit closest separable state.

• Quantum Resource Theory
• Entanglement measures
• Quantum separability
• Quantum relative entropy

What is the exact LOCC distillable entanglement \(E_D(\rho_{\mathrm{as}}^{(d)})\) of the \(d\times d\) antisymmetric state, for each integer \(d\ge3\)?

• Quantum Resource Theory
• Entanglement distillation
• Entanglement measures
• Local operations and classical communication
• PPT-preserving operations

Can discarding one local qubit reduce two-way distillable entanglement by an arbitrarily large amount?

• Quantum Resource Theory
• Entanglement distillation
• Entanglement measures
• Local operations and classical communication