Deterministic secure quantum communication against collective noise

Collective noise is one of the main obstacles that reduce the efficiency of quantum communication. In this paper, we present two robust deterministic secure quantum communication (DSQC) schemes based on logical qubits. The first scheme employs a store-and-measure strategy along with the exclusive OR operation. Then we propose a second scheme without storage by exploiting hidden permutations and one-way hash functions. To achieve the performance of robustness against collective noise, both schemes take advantage of the compensability of decoherent-free subspace (DFS) for noise. Moreover, except for decoy qubits, all quantum states are used to convey the secret message. In addition, we provide a rigorous security analysis of potential attacks and prove the security of our protocols.