Abstract
We present two robust quantum key distribution protocols against two kinds of collective noise, following some ideas in quantum dense coding. Three-qubit entangled states are used as quantum information carriers, two of which form the logical qubit, which is invariant with a special type of collective noise. The information is encoded on logical qubits with four unitary operations, which can be read out faithfully with Bell-state analysis on two physical qubits and a single-photon measurement on the other physical qubit, not three-photon joint measurements. Two bits of information are exchanged faithfully and securely by transmitting two physical qubits through a noisy channel. When the losses in the noisy channel is low, these protocols can be used to transmit a secret message directly in principle.
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