Generalized flying-qudit scheme in arbitrary dimensions

Abstract

We generalize in higher dimensions the so-called "flying-qubit scheme" that was described in the paper by Lim, Beige, and Kwek [Phys. Rev. Lett. 95, 030505 (2005)]. In that paper, the authors proposed a scheme according to which distant atoms get entangled during a measurement, in the Bell basis, of photons (flying qubits) emitted by them. We show that although in principle a generalization of this scheme to arbitrary dimensions is possible, this theoretical proposal is not presently feasible in all dimensions because only qubit Bell states have been successively measured until now. Nevertheless we show that a many-qubits generalization of the flying-qubit scheme factorizes and reduces to the realization, in parallel, of many individual single-qubit schemes, for which it is known that they are realizable experimentally with the techniques that are available today. In other words, our approach shows that when d is an even prime power (d= 2m), the flying-qudit scheme reduces to m flying-qubit schemes. For d= 2m and arbitrary m the implementation of a generalized, maximally entangling, conditional qudit phase gate "with insurance" or "repeat-until-success" is thus shown to be feasible in practice by coupling m (pairs of) two-level atoms to m (pairs of) two-level (polarized) photons. Moreover, due to the parallelism of the task, the time necessary for completing successfully the task scales logarithmically in a function of m while at the same time the dimension of the Hilbert space scales exponentially which presents promising perspectives regarding quantum informational realizations such as the quantum computer. © 2008 The American Physical Society.