Towards Additivity of Entanglement of Formation

Keiji Matsumoto, Toshiyuki Shimono, Andreas Winter

Shao-Ming Fei, Zhi‐Xi Wang, Hui Zhao

Li-Jun Zhao, Lin Chen

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 ${\mathbb{C}}^{m}\ensuremath{\bigotimes}{\mathbb{C}}^{3}$, and the two-dimensional EB space in ${\mathbb{C}}^{2}\ensuremath{\bigotimes}{\mathbb{C}}^{n}$. 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 arbitrarily given dimensions. We show that the example in Phys. Rev. Lett. 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 Tavis-Cummings model.

A. A. Pomeransky

The additivity of both the entanglement of formation and the classical channel capacity is known to be a consequence of the strong superadditivity conjecture. We show that, conversely, the strong superadditivity conjecture follows from the additivity of the entanglement of formation; this means that the two conjectures are equivalent and that the additivity of the classical channel capacity is a consequence of them.

Koenraad M.R. Audenaert, Samuel L. Braunstein

Shao-Ming Fei, Jürgen Jost, Xianqing Li‐Jost +1 more