Analysis of the role of von Neumann's projection postulate in the canonical scheme of quantum teleportation and main quantum algorithms

TL;DR

This paper critically examines the role of von Neumann's projection postulate in quantum teleportation and algorithms, revealing that teleportation is impossible under this postulate while quantum algorithms remain consistent.

Contribution

It clarifies the foundational role of von Neumann's postulate in quantum information processes, challenging the feasibility of quantum teleportation within this framework.

Findings

Quantum teleportation is impossible in von Neumann's framework.

Main quantum algorithms are consistent with von Neumann's projection postulate.

Analysis highlights foundational issues in quantum information theory.

Abstract

Modern development of quantum technologies based on quantum information theory stimulated analysis of proposed computational, cryptographic and teleportational schemes from the viewpoint of quantum foundations. It is evident that not all mathematical calculations performed in complex Hilbert space can be directly realized in physical space. Recently by analyzing the original EPR paper we found that they argument was based on the misuse of the von Neumann's projection postulate. Opposite to von Neumann, Einstein, Podolsky and Rosen (EPR) applied this postulate to observables represented by operators with degenerate spectra. It was completely forbidden by von Neumann's axiomatics of QM. It is impossible to repeat the EPR considerations in the von Neumann's framework. In this note we analyze quantum teleportation by taking into account von Neumann's projection postulate. Our analysis shows that so called quantum teleportation is impossible in von Neumann's framework. On the other hand, our analysis implies that the main quantum algorithms are totally consistent with von Neumann's projection postulate.