Generalized possibilistic Theories: the multipartite experiments problem

TL;DR

This paper extends the framework of Generalized Possibilistic Theories by axiomatizing tensor products of state spaces, addressing bipartite experiments, and exploring their mathematical structure to aid quantum theory reconstruction.

Contribution

It provides an axiomatic construction of tensor products in possibilistic theories and explores their properties, advancing the foundation for quantum theory reconstruction within this framework.

Findings

Explicit constructions of tensor products of Inf semi-lattices.

Analysis of tensor products of orthocomplemented Inf semi-lattices.

First steps towards a quantum theory reconstruction program.

Abstract

In a recent paper, the author introduced an operational description of physical theories where probabilities are replaced by counterfactual statements belonging to a three-valued (i.e. possibilistic) semantic domain. The complete axiomatic of these Generalized possibilistic Theories is generalized and clarified in the present paper. The problem of bipartite experiments is then addressed as the main skill of this paper. An axiomatic for the tensor product of our spaces of states is given and different solutions are explicitly constructed. This description of tensor products of Inf semi-lattices is partly independent from the usual mathematical description of this problem. The nature of the tensor product of orthocomplemented Inf semi-lattices is then also explored. This subject is indeed fundamental for the development of a reconstruction program for quantum theory within our framework. Our analysis constitutes a first step towards this achievement.