Non-classical conditional probability and the quantum no-cloning theorem

TL;DR

This paper generalizes the quantum no-cloning theorem within a broader framework of quantum logics using conditional probability calculus, avoiding reliance on tensor products or finite dimensions.

Contribution

It introduces a generalized form of the no-cloning theorem applicable to quantum logics with conditional probability, expanding its theoretical scope.

Findings

Generalization of the no-cloning theorem to abstract quantum logics.

Avoidance of tensor product and finite-dimensional assumptions.

Provides a simple, foundational approach to quantum logic and cloning constraints.

Abstract

The quantum mechanical no-cloning theorem for pure states is generalized and transfered to the quantum logics with a conditional probability calculus in a rather abstract, though simple and basic fashion without relying on a tensor product construction or finite dimension as required in other generalizations.