Efficient protocols for unidirectional and bidirectional controlled deterministic secure quantum communication: different alternative approaches

Recently, Hassanpour and Houshmand have proposed a protocol of controlled deterministic secure quantum communication (Hassanpour and Houshmand, Quantum Inf Process 14:739–753, 2015). The authors compared the efficiency of their protocol with that of two other existing protocols and claimed that their protocol is efficient. Here, we have shown that the efficiency of Hassanpour Houshmand (HH) protocol is not high, and there exist several approaches through which more efficient protocols for the same task can be designed. To establish this point, we have proposed an efficient protocol of controlled deterministic secure quantum communication which is based on permutation of particles technique and is considerably efficient compared to HH protocol. We have also generalized this protocol into its bidirectional counterpart. Interestingly, bipartite entanglement (Bell state) is sufficient for the realization of the proposed protocols, but HH protocol and other existing protocols require at least tripartite entanglement. Further, we have shown that it is possible to construct a large number of efficient protocols of unidirectional and bidirectional controlled deterministic secure quantum communication by using various alternative approaches and different quantum states. These alternative protocols can be realized by modifying the existing protocols of quantum secure direct communication and deterministic secure quantum communication. We have also shown that it is possible to design completely orthogonal-state-based protocols for unidirectional and bidirectional controlled deterministic secure quantum communication.