ua nt - p h / 00 05 06 8 v 1 1 7 M ay 2 00 0 On Teleportation of a Completely Unknown State of Relativistic Photon

The process of teleportation of a completely unknown single-photon relativistic state is considered. Analysis of the relativistic case reveals that the teleportation as it is understood in the non-relativistic quantum mechanics is impossible if no a priori information on the state to be tele-ported is available. It is only possible to speak of the amplitude of the propagation of the field (taking into account the measurement procedure) since the existence of a common vacuum state together with the microcausality principle (the field operators commutation relations) make the concept of the propagation amplitude for the individual subsystems physically meaningless. When partial a priori information is available (for example, only the polarization state of the photon is unknown while its spatial state is specified beforehand), the teleportation does become possible in the relativistic case. In that case the a priori information can be used to " label " the identical particles to make them effectively distinguishable. One of the basic results of the non-relativistic quantum information theory consists in the possibility of the ideal teleportation of an unknown quantum state by means of a classical and distributed quantum communication channel [1]. The latter is realized by a non-local entangled state (an EPR-pair [2]). The teleportation of an unknown quantum state from the user A to user B is performed in the following way [1]. The user A has a quantum system 1 in an unknown state ρ 1 (for example, a spin-1/2 particle) whose state is to be teleported to user B. To do this, the user A prepares a composite system consisting of the two particles 2 and 3 in a maximally entangled state ρ 23 (EPR-pair) so that the user B can only access the particle 3 while the particles 1 and 2 remain available to user A. Then user A performs an appropriate joint measurement over the particles 1 (whose state is to be teleported) and 2. The measurement brings the composite system consisting of the particles 1, 2, and 3 from the initial state ρ 1 ⊗ ρ 23 to the new state ρ ′ 123 which depends on the measurement outcome i (in the teleportation of the system described by a finite-dimensional state space the set of all possible outcomes is discrete). The crucial point here is the existence of the measurements possessing the special property that the state of the third particle after the measurement ρ …