Spacetime symmetries and the qubit Bloch ball: a physical derivation of finite dimensional quantum theory and the number of spatial dimensions

Abstract

Quantum theory and relativity are the pillar theories on which our understanding of physics is based. Poincaré invariance is a fundamental physical principle stating that the experimental results must be the same in all inertial reference frames in Minkowski spacetime. It is a basic condition imposed on quantum theory in order to construct quantum field theories, hence, it plays a fundamental role in the standard model of particle physics too. As is well known, Minkowski spacetime follows from clear physical principles, like the relativity principle and the invariance of the speed of light. Here, we reproduce such a derivation, but leave the number of spatial dimensions $n$ as a free variable. Then, assuming that spacetime is Minkowski in $1+n$ dimensions and within the framework of general probabilistic theories, we reconstruct the qubit Bloch ball and finite dimensional quantum theory, and obtain that the number of spatial dimensions must be $n=3$, from Poincaré invariance and other physical postulates. Our results suggest a fundamental physical connection between spacetime and quantum theory.

Accepted manuscript. To appear in Physical Review A

References in corpus (8)

• Characterizing quantum theory in terms of information-theoretic constraints
• A derivation of quantum theory from physical requirements
• A generalized no-broadcasting theorem
• Towards Quantum Gravity: A Framework for Probabilistic Theories with Non-Fixed Causal Structure
• Higher-order interference and single-system postulates characterizing quantum theory
• On quantum vs. classical probability
• Quantum theory from rules on information acquisition
• Information and communication in polygon theories