Dual- and Multi-rail Encoding

We review the dual-rail encoding (Burgarth and Bose, Phys Rev A 71:052315, 2005) which demonstrates how the problem of dispersion in quantum state transfer in spin chain communication can be attacked and overcome through performing measurements at the receiver side. We discuss the performance of the dual-rail technique in detail with respect to noise, disorder in the chain couplings (Burgarth and Bose, New J Phys 7:135, 2005) and deviations from a strict one-dimensionality. We then show how the dual-rail method can be made more efficient by using multiple channels (Burgarth et al., Int J Quant Inf 4:405, 2006; J Phys A Math Gen 38:6793, 2005). We provide a convergence theorem which shows that any nearest-neighbor excitation preserving chain is capable of efficient and perfect state transfer using a multi-rail encoding.