We propose a two-step quantum secure direct communication （QSDC） protocol with hyperentanglement in both the spatial-mode and the polarization degrees of freedom of photon pairs which can in principle be produced with a beta barium borate crystal. The secret message can be encoded on the photon pairs with unitary operations in these two degrees of freedom independently. This QSDC protocol has a higher capacity than the original two-step QSDC protocol as each photon pair can carry 4 bits of information. Compared with the QSDC protocol based on hyperdense coding, this QSDC protocol has the immunity to Trojan horse attack strategies with the process for determining the number of the photons in each quantum signal as it is a one-way quantum communication protocol.
Based on a simple classical model specifying that the primary electrons interact with the electrons of a lattice through the Coulomb force and a conclusion that the lattice scattering can be ignored, the formula for the average energy required to produce a secondary electron （ε） is obtained. On the basis of the energy band of an insulator and the formula for e, the formula for the average energy required to produce a secondary electron in an insulator （εi） is deduced as a function of the width of the forbidden band （Eg） and electron affinity X. Experimental values and the εi values calculated with the formula are compared, and the results validate the theory that explains the relationships among Eg, X, and ei and suggest that the formula for εi is universal on the condition that the primary electrons at any energy hit the insulator.
Based on the main physical processes,we deduce the relationships among the incident energy Wp0 of the primary electron,the number of released secondary electrons(i.e.δ_(PEθ))per primary electron entering the metal at incident angleθand the angleθitself.In addition,the relationship ofδPEθatθ=0°,i.e.δ_(PE0),with Wp0 is determined.From the experimental results,the relationship of the ratio atθ=0°,i.e.β_(0) which is the ratio of the average number of released secondary electrons generated by a single primary electron backscattered at the metal surface to that generated by a single primary electron entering the metal,with Wp0 is determined.Moreover,the relationships among the ratioβθ,Wp0 andθare obtained.Based on the relationships among the secondary electron yield atθ(i.e.δθ),the yield atθ=0°(i.e.δ_(0)),the backscattering coefficient atθ(i.e.η_(θ)),the coefficient atθ=0°(i.e.η0),δ_(PEθ)andδ_(PE0),we deduce the universal formula forδ_(θ),δ_(0),η_(θ),η_(0),and W_(p0) for the primary electrons at an incident energy of 2–10 keV.The secondary electron yields calculated from the universal formula and the experimental yields of some metals are compared,and the results suggest that the proposed formula is universal for estimation of secondary electron yields atθ=0°−80°.
We present two robust quantum secure direct communication (QSDC) schemes with a quantum one-time pad over a collective-noise channel. Each logical qubit is made up of two physical qubits and it is invariant over a collective-noise channel. The two photons in each logical qubit can be produced with a practically entangled source, i.e., a parametric down-conversion source with a beta barium borate crystal and a pump pulse of ultraviolet light. The information is encoded on each logical qubit with two logical unitary operations, which will not destroy the antinoise feather of the quantum systems. The receiver Bob can read out the sender's message directly with two single-photon measurements on each logical qubit, instead of Bell-state measurements, which will make these protocols more convenient in a practical application. With current technology, our two robust QSDC schemes are feasible and may be optimal ones.
