Quantum Key Distribution in the Holevo Limit

Abstract

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 $E\le 1$. The problem addressed here is whether the limit $E=1\mathrm{}$ 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 $E=1\mathrm{}$ based on polarized photons and in which Bob's state discrimination can be implemented with linear optical elements is presented.