Violação da superaditividade forte do emaranhamento quântico

Abstract

Over two decades, it has been discussing whether the entanglement can bring advan- tages to the capacity of classical communication over a quantum channel. Today it

is already known that some improvement in the capacity is possible, though is not known under what conditions and how significant it can be. The main purpose here is to discuss this question. Particularly, we review three mathematical statements which

are equivalente and address the problem: The additivity of Holevo Capacity; the ad- ditivity of Entanglement of Formation; and the inequality of Strong Superadditivity of

the Entanglement of Formation. A counter-example to any of these question implies a counter-example to the others and a possible improvement in the capacity of a quantum channel using entanglement. After that, we focus and the latter statement. Using the Rényi measure of entanglement, a generalisation of the Entanglement of Formation, we construct simple states that violates the Strong Superadditivity inequality with this measure. These states are shown to exist for all order parameter of the Rényi measure, α > 1. Unfortunately, when α → 1, the limit in which the Rényi measure tends to the Entanglement of Formation, the violation is shown to disappears. Nevertheless, simple and analytically manipulable examples can be very useful in understanding this difficult problem.