Quantum / CONCEPT

Optimality of the coefficient in the entanglement-breaking norm inequality

For every dimension d ≥ 2, every Hermitian traceless basis λ₁, …, λ_{d²−1} with tr(λᵢλⱼ) = 2δᵢⱼ and every real B > d(d − 1)/2, some entanglement-breaking channel has Bloch data (A, c) with ‖A‖_*² + B|c|² > (d − 1)²; hence d(d − 1)/2 is the largest coefficient of |c|² for which the norm inequality for entanglement-breaking channels can hold.