arXiv:1611.02515 [quant-ph]
arXiv:1611.02926 [quant-ph]

In these papers I consider

- the quantum no-cloning theorem,
- two quantum key distribution protocols (BB84 and E91),
- entanglement assisted quantum teleportation, and
- Grover's search algorithm

I show that neither the wavefunction nor Hilbert spaces nor operator algebras are needed to treat all these well-known quantum mechanical features. A much more general and abstract access is possible than commonly thought.

The only thing that is needed is a non-classical extension of conditional probability, which can be considered as a generalized model of projective quantum measurement (Lüders - von Neumann measurement process).

This approach may help to understand the deeper origins of the above quantum mechanical features as well as of quantum measurement and may perhaps do so better than the usual Hilbert space formalism which is so overly rich in mathematical structure that, as the saying goes, one does not see the wood for the trees.