Local theories with parallel realities and the epistemic view of the quantum state

TL;DR

This paper proposes a hybrid framework combining elements of single-world and many-worlds quantum theories to address nonlocality and interpretative issues, enabling local models with finite information flow and deriving quantum probabilities from ensemble averages.

Contribution

It introduces a novel hybrid theoretical framework that unifies aspects of single-world and many-worlds theories, addressing nonlocality and interpretative challenges in quantum mechanics.

Findings

A local model for entangled qubits with only one bit of communication.

The framework allows deriving quantum probabilities from ensemble averages.

It reduces information flow compared to previous theories.

Abstract

Hidden-variable theories effectively solve the measurement problem. However, a serious issue of this route towards a realistic completion of quantum theory is raised by Bell's proof that the resulting theories are nonlocal. A possible resolution is to reject the assumption that measurements have single actual outcomes. Indeed, relaxing this premise, Deutsch and Hayden showed that Bell's theorem can be evaded by delaying the buildup of the correlations until the parties compare their outcomes at a meeting point. However, the Deutsch-Hayden theory, which is deterministic and psi-ontic, leads to an infinite information flow towards the meeting point. Furthermore, alternative branches are weighted by amplitudes, leading to interpretative issues. In this paper, we introduce a general framework that combines the randomness of single-world theories with the coexistence of diverse instances, as found in many-worlds theory. This framework incorporates the existing theories as limiting cases. We explore how this hybrid approach addresses key challenges of single-world and Deutsch-Hayden theories. On one hand, the multiplicity of coexisting instances allows us to circumvent nonlocality and, possibly, contextuality. On the other hand, randomness makes it possible to derive quantum probabilities from unweighted counts of instances and ensemble averages. Furthermore, it can lead to a reduction of the information flow. We illustrate this framework with a local model for two spatially separate maximally entangled qubits. The model requires two unweighted instances and a finite information flow -- just one bit per measurement is communicated to the meeting point. Setting aside its foundational motivations, this framework has also relevance in quantum communication complexity and leads to novel technical questions, potentially providing new insights into some peculiarities of entanglement.