Quantum teleportation and Grover's algorithm without the wavefunction

TL;DR

This paper generalizes quantum teleportation and Grover's algorithm using an abstract framework that extends beyond traditional quantum mechanics, employing non-classical conditional probabilities instead of wavefunctions.

Contribution

It introduces a novel abstract approach to quantum information protocols, removing reliance on wavefunctions and Hilbert spaces, thus broadening the conceptual foundation of quantum mechanics.

Findings

Quantum protocols can be reformulated in an abstract setting.

The approach encompasses standard quantum mechanics as a special case.

Non-classical conditional probabilities replace wavefunctions in the framework.

Abstract

In the same way as the quantum no-cloning theorem and quantum key distribution in two preceding papers, entanglement-assisted quantum teleportation and Grover's search algorithm are generalized by transferring them to an abstract setting, including usual quantum mechanics as a special case. This again shows that a much more general and abstract access to these quantum mechanical features is possible than commonly thought. A non-classical extension of conditional probability and, particularly, a very special type of state-independent conditional probability are used instead of Hilbert spaces and wavefunctions.