Improving the capacity of the ping-pong protocol

Since Bennett and Brassard presented the pioneer quantum key distribution (QKD) protocol in 1984 [1], there are a lot of theoretical QKD schemes [1-12] today. Recently, Beige et al. proposed a quantum secure direct communication scheme [13], which allows messages communicated directly without first establishing a random key to encrypt them. Bostroem and Felbingeer presented a ping-pong protocol [14] which is secure for key distribution and quasisecure for direct communication with a perfect quantum channel. However, an eavesdropper-Eve can eavesdrop the information if the quantum channel is noisy [15]. And this ping-pong protocol can attacked without eavesdropping [16]. Moreover, the capacity is restricted, and an entangled state only carries one bit of classical information in every message run. In this paper, we give an improved ping-pong protocol, which allows one entangled state carrying two classical bits in every message run. And we show this protocol is secure with a classical message authentification method. Let us start with the brief description of the ping-pong protocol. Suppose Bob have two photons that are maximally entangled in their polarization degree of freedom, |ψ± >= 1 √ 2 (|1 > |0 > ±|0 > |1 >). Since the reduced density matrices, ρA = trB{|ψ± >< ψ±|} are completely mixture, then one can not distinguish the state |ψ± > from each other by only access one qubit. Since the state |ψ± > are mutually orthogonal , a measurement on both qubit can perfectly distinguish the states form each other. Bob sends one of the photon (travel photon) to Alice and keeps another (home qubit). Alice can performs a unitary operation Uj,