  The process of teleportation of a completely unknown one-particle state of a
free relativistic quantum field is considered. In contrast to the
non-relativistic quantum mechanics, the teleportation of an unknown state of
the quantum 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 state
of the EPR-pair belong. The reason is of the existence of a cyclic (vacuum)
state common to both the unknown state and the EPR-pair. Due to the common
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 the relativistic
theory the teleportation in the sense it is understood in the non-relativistic
quantum mechanics proves to be impossible because of the impossibility of the
realization of the appropriate measurement as a tensor 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 whole.
