ar X iv : q ua nt - p h / 98 10 00 1 v 1 1 O ct 1 99 8 A posteriori teleportation

The article by Bouwmeester et al. on experimental quantum teleportation constitutes an important advance in the burgeoning field of quantum information. The experiment was motivated by the proposal of Bennett et al. in which an unknown quantum state is ‘teleported’ by Alice to Bob. As illustrated in Fig. 1, in the implementation of this procedure, by Bouwmeester et al., an input quantum state is ‘disembodied’ into quantum and classical components, as in the original protocol. However, in contrast to the original scheme, Bouwmeester et al.’s procedure necessarily destroys the state at Bob’s receiving terminal, so a ‘teleported’ state can never emerge as a freely propagating state for subsequent examination or exploitation. In fact, teleportation is achieved only as a postdiction. Bouwmeester et al. used parametric down-conversion from two sources (SI, SII in Fig. 1) in an attempt to teleport the polarization state of a single-photon wavepacket (in beam 1) from Alice’s sending station to Bob’s receiving station (in beam 3). Statistics consistent with teleportation are obtained for events with a fourfold coincidence (from detectors f1 and f2, d1 or d2, and p). We ask whether the detection of all four quanta is essential for teleportation in this scheme. To answer this question, we calculated the teleportation fidelity, F , when the coincidence condition is relaxed to exclude detection at Bob’s station (d1, d2). Under relaxed conditions, requiring only threefold coincidence of detectors p and (f1, f2), teleportation is achieved when the fields of beams 1 and 3 match with sufficiently high fidelity. In the simplest approximation, type II parametric down-conversion on modes (i, j) generates wavepacket states as follows: