Weakening the Born Rule - Towards a Stateless Formulation of Quantum Mechanics

TL;DR

This paper proposes a novel formulation of quantum mechanics that replaces the traditional state vector with assertions about measurement outcomes, aiming to address foundational issues related to the notion of quantum state.

Contribution

It introduces a state-free approach based on verification assertions and logical rules to reason about quantum systems without referencing the problematic state vector.

Findings

Develops a logical framework using verification assertions

Replaces the notion of quantum state with measurement outcome assertions

Provides a new perspective on quantum foundations

Abstract

The notion of state vector is, in quantum mechanics, as central as it is problematic, as illustrates the wealth of publications about the sub- jects, including in particular the many attempts to obtain an acceptable interpretation of quantum mechanics. In this article, we propose a different approach, and initiate the study of a formulation of quantum mechanics, where the notion of state is entirely replaced by assertions about measurement outcomes. We define a notion of "verification" which represents the knowledge that one may have about the possible outcomes of the measurements performed on a quantum system, and express a set of logical rules which allow to reason about quantum systems using verification assertions only, and thus making no reference to the problematic notion of state.