Quantum Key Distribution in the Holevo Limit

A theorem by Shannon and the Holevo theorem impose that the efficiency of any protocol for quantum key distribution, E, defined as the number of secret (i.e., allowing eavesdropping detection) bits per transmitted bit plus qubit, is E≤1. The problem addressed here is whether the limit E  =  1 can be achieved. It is showed that it can be done by splitting the secret bits between several qubits and forcing Eve to have only a sequential access to the qubits, as proposed by Goldenberg and Vaidman. A protocol with E  =  1 based on polarized photons and in which Bob's state discrimination can be implemented with linear optical elements is presented.