Robust quantum secure direct communication with a quantum one-time pad over a collective-noise channel

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.