Output state in multiple entanglement swapping

Abstract

The technique of quantum repeaters is a promising candidate for sending quantum states over long distances through a lossy channel. The usual discussions of this technique deals with only a finite dimensional Hilbert space. However the qubits with which one implements this procedure will "ride" on continuous degrees of freedom of the carrier particles. Here we analyze the action of quantum repeaters using a model based on pulsed parametric down conversion entanglement swapping. Our model contains some basic traits of a real experiment. We show that the state created, after the use of any number of parametric down converters in a series of entanglement swappings, is always an entangled (actually distillable) state, although of a different form than the one that is usually assumed. Furthermore, the output state always violates a Bell inequality.