Remarks on additivity of the Holevo channel capacity and of the entanglement of formation

The purpose of these notes is to discuss the relation between the additivity questions regarding the quantities (Holevo) capacity of a quantum channel T and entanglement of formation of a given bipartite state. In particular, using the Stinespring dilation theorem, we give a formula for the channel capacity involving entanglement of formation. This can be used to show that additivity of the latter for some states can be inferred from the additivity of capacity for certain channels. We demonstrate this connection for a family of group--covariant channels, allowing us to calculate the entanglement cost for many states, including some where a strictly smaller upper bound on the distillable entanglement is known. This is presented in a general framework, extending recent findings of Vidal, Dur and Cirac (e-print quant-ph/0112131). In an appendix we speculate on a general relation of superadditivity of the entanglement of formation, which would imply both the general additivity of this function under tensor products and of the Holevo capacity (with or without linear cost constraints)

Entanglement Cost of Antisymmetric States and Additivity of Capacity of Some Quantum Channel

We study the entanglement cost of the states in the contragredient space, which consists of $(d-1)$ $d$-dimensional systems. The cost is always $\log_2 (d-1)$ ebits when the state is divided into bipartite \C^d \otimes (\C^d)^{d-2}. Combined with the arguments in \cite{Matsumoto02}, additivity of channel capacity of some quantum channels is also shown.Comment: revtex 4 pages, no figures, small changes in title and author's affiliation and some typo are correcte