A scheme for total quantum teleportation

We address the issue of totally teleporting the quantum state of an external particle, as opposed to studies on partial teleportation of external single-particle states, total teleportation of coherent states and encoded single-particle states, and intramolecular teleportation of nuclear spin states. We find a set of commuting observables whose measurement directly projects onto the Bell-basis and discuss a possible experiment, based on two-photon absorption, allowing, for the first time, total teleportation of the state of a single external photon through a direct projective measurement. Teleportation, in its present formulation, is an event by which a more or less complex physical object is transferred from one point in space to another without its actual material transportation. From a classical perspective, there is no conceptual impediment to teleportation: a system can be thoroughly scanned in a given location, and completely reconstructed in a second site, transmitting only the characterizing information but not the actual constituents. This procedure is evidently invalid for any real physical system, since its intrinsic quantum content cannot be generally measured and reconstructed. Remarkably, in the extreme (but intrinsic to any complex system) microscopic case of an unknown quantum state of a single external particle, Bennett et al. [1] have unveiled how quantum theory permits the “teleportation” of the state through the direct transmission of only classical information, whereas the quantum content is sent through an Einstein-Podolski-Rosen (EPR) two-particle entangled state [2]. In this formulation, two spin 1/2 particles 1 and 2 are prepared in the EPR singlet-state <2 3 2 3 2 3 1 2 , / n p p n . (1) Particle 2 is directed towards a region in which an experimenter called Alice is located, whereas the correlated particle 3 is sent to Bob. Alice is given a second (quantum) particle, labeled particle 1, wholly uncorrelated to 2 and 3, in an unknown spin state I1 1 1 n p a b , (2) where a and b are two unknown c numbers ( a b 2 2 1 ). Let Alice perform an experiment on the system of particles 1 and 2 she has available, projecting on the Bell-operator basis [3] described by the two particle states <1 2 1 2 1 2 1 2 , / r n p r p n )1 2 1 2 1 2 1 2 , / r n n r p p . (3) Since the three particle system is described by the wavefunction