Perfect state transfer in networks of arbitrary topology and coupling configuration

A general formalism of the problem of perfect state transfer is presented. We show that there are infinitely many Hamiltonians that may provide a solution to this problem. In a first attempt to give a classification of them we investigate their possible forms and the related dynamics during the transfer. Finally, we show how the present formalism can be used for the engineering of perfect quantum wires of various topologies and coupling configurations.

Figure 1

Evolution of the occupation probability distribution governed by PST Hamiltonians of various spectra. Each plot corresponds to a network of eleven sites and 500 successive applications of the corresponding PST Hamiltonian. While the monotonously decreasing spectrum induces a rather simple diagonal pattern (a), the other types of spectra induce more complicated patterns. Because all the Hamiltonians involve, in general, nonvanishing couplings between the various sites, the wave packet can spread rapidly to distant sites as can be seen from plots (b)–(d).

Figure 2

Evolution of the overall concurrence corresponding to Figs. 1a, 1b, 1c, as a function of iterations.