Analysis of the role of von Neumann’s projection postulate in the canonical scheme of quantum teleportation

Abstract

Modern development of quantum technologies based on quantum information theory (in particular, laser-based quantum-information technologies) stimulated the analysis of proposed computational, cryptographic, and teleportational schemes from the viewpoint of quantum foundations. It is evident that not all mathematical calculations performed in the complex Hilbert space can directly be realized in the physical space. Recently, analyzing the original EPR paper, we found that their argument was based on the misuse of von Neumann’s projection postulate. In contrast to von Neumann, Einstein, Podolsky, and Rosen (EPR) applied this postulate to the observables represented by the operators with degenerate spectra. It was completely forbidden by von Neumann’s axiomatics of quantum mechanics. It is impossible to repeat the EPR considerations within the von Neumann’s framework. We analyze here quantum teleportation by taking into account von Neumann’s projection postulate. Our analysis shows that the so-called quantum teleportation is impossible within the von Neumann’s framework.