Dense quantum communication using single- and two-particle operations on six-particle cluster state

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Theory of controlled tripartite quantum dense coding for the transmission of four-binary bits between two distinct locations is presented. The entanglement resource for this transmission is provided by a six-qubit cluster state. Theoretical detail of an encoder that can encode sixteen different operations and a four-bit binary decoder required for this transmission is discussed. We show that in the absence of availability of any four-state analyzer decoding can be reduced to single-particle and two-particle Bell-state measurements ( BSM ). In our scheme, Bell-state measurements ( BSM ) performed during decoding, result in Bell-pairs, which along with single-particle projections are used to unambiguously discriminate all sixteen encoding operations. Proposed experiment to verify theory of tripartite quantum dense coding scheme, using photonic entanglement, is also briefly discussed. Success probability of the scheme is determined. In addition, long-distance implementation of this tripartite quantum dense coding scheme is discussed. Fault-tolerant quantum repeaters used in this long-distance scheme are based on quantum errorcorrection, which is achieved with the aid of Calderbank-Shor-Steane ( CSS ) encoding.