Additivity of entanglement of formation via entanglement-breaking space

Abstract

We study the entanglement-breaking (EB) space, such that the entanglement of formation (EOF) of a bipartite quantum state is additive when its range is an EB subspace. We systematically construct the EB spaces in the Hilbert space ${\mathbb{C}}^m\otimes {\mathbb{C}}^3$, and the $2$-dimensional EB space in ${\mathbb{C}}^2\otimes {\mathbb{C}}^n$. We characterize the expression of two-qubit states of rank two with nonadditive EOF, if they exist. We further apply our results to construct EB spaces of an arbitrarily given dimensions. We show that the example in [PRL 89,027901(2002)] is a special case of our results. We further work out the entanglement cost of a qubit-qutrit state in terms of the two-atom system of the .

References in corpus (8)

• Measuring Quantum Coherence with Entanglement
• Conservation law for distributed entanglement of formation and quantum discord
• Strong superadditivity of the entanglement of formation follows from its additivity
• Qubit-qudit states with positive partial transpose
• Classification of multipartite entanglement containing infinitely many kinds of states
• The strong superadditivity conjecture holds for the quantum depolarizing channel in any dimension
• Quantum states representing perfectly secure bits are always distillable
• The Birkhoff theorem for unitary matrices of arbitrary dimensions