We present a quantum communication protocol which keeps all the properties of the ping-pong protocol [Phys. Rev. Lett. 89, 187902 (2002)] but improves the capacity doubly as the ping-pong protocol. Alice and Bob can use the variable measurement basises in control mode to detect Eve's eavesdropping attack. In message mode, Alice can use one unitary operations to encode two bits information. Bob only needs to perform a Bell type measurement to decode Alice's information. A classical message authentification method can protect this protocol against the eavesdropping hiding in the quantum channel losses and the denial-of-service (DoS) attack.Since Bennett and Brassard presented the pioneer quantum key distribution (QKD) protocol in 1984 [1], there are a lot of theoretical QKD schemes [1][2][3][4][5][6][7][8][9][10][11][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,Since the reduced density matrices, ρ A = tr B {|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 U j ,

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A comprehensive set of transition probabilities and radiative lifetimes of Rydberg states of alkali atoms (for Na, K, Cs, n 30; and for Rb, n 6 50) is obtained by using a simple, exactly solvable potential model for atoms. The results agree well with the available experimental values and other theoretical ones. Scaling relations for evaluating transition probabilities and lifetimes of high Rydberg states are also discussed. The well known (n*)-' scaling law of the transition probabilities A,,,,. with n'= n >> 1 is generally valid; however, we also find deviations from this law for some d-, p and f-* d transitions for Rb. A third-power polynomial is found to be better than the currently used exponential scaling law in predicting the lifetimes of even higher excited states.

Equilibrium distances, binding energies and dissociation energies for the ground and low-lying states of the hydrogen molecular ion in a strong magnetic field parallel to the internuclear axis are calculated and refined, by using the two-dimensional pseudospectral method. High-precision results are presented for the binding energies over a wider field regime than already given in the literature (Kravchenko and Liberman 1997 Phys. Rev. A 55 2701). The present work removes a long-standing discrepancy for the Req value in the 1σu state at a field strength of 1.0 × 106 T. The dissociation energies of the antibonding 1πg state induced by magnetic fields are determined accurately. We have also observed that the antibonding 1πg potential energy curve develops a minimum if the field is sufficiently strong. Some unreliable results in the literature are pointed out and discussed. A way to efficiently treat vibrational processes and coupling between the nuclear and the electronic motions in magnetic fields is also suggested within a three-dimensional pseudospectral scheme.

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