Teleportation of the relativistic quantum field

The process of teleportation of a completely unknown one-particle state of a free relativistic quantum field is considered. In contrast to the non-rel ativistic quantum mechanics, the teleportation of an unknown state of the q uantum field cannot be in principle described in terms of a measurement in a tensor product of two Hilbert spaces to which the unknown state and the s tate of the EPR-pair belong. The reason is of the existence of a cyclic (va cuum) state common to both the unknown state and the EPR-pair. Due to the c ommon vacuum vector and the microcausality principle (commutation relations for the field operators), the teleportation amplitude contains inevitably contributions which are irrelevant to the teleportation process. Hence in t he relativistic theory the teleportation in the sense it is understood in t he non-relativistic quantum mechanics proves to be impossible because of th e impossibility of the realization of the appropriate measurement as a tens or product of the measurements related to the individual subsystems so that one can only speak of the amplitude of the propagation of the field as a w hole. (C) 2000 Elsevier Science B.V. All rights reserved.