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.

arXiv commentAccepted manuscript. To appear in Physical Review A

References in corpus (52)

• Information Causality as a Physical Principle
• Informational derivation of Quantum Theory
• Non-local correlations as an information theoretic resource
• Probabilistic theories with purification
• A systematic approach to generalisations of General Relativity and their cosmological implications
• 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
• Local Quantum Measurement and No-Signaling Imply Quantum Correlations
• Higher-order interference and single-system postulates characterizing quantum theory
• Existence of an information unit as a postulate of quantum theory
• A Quantum-Bayesian Route to Quantum-State Space
• Entropy and Information Causality in General Probabilistic Theories
• Quantum theory from questions
• All reversible dynamics in maximally non-local theories are trivial
• Entropy in general physical theories
• Limits on non-local correlations from the structure of the local state space
• Generalized Probabilistic Theories Without the No-Restriction Hypothesis
• Unified Framework for Correlations in Terms of Local Quantum Observables
• Generalised phase kick-back: the structure of computational algorithms from physical principles
• Deriving quantum theory from its local structure and reversibility
• An Information-Geometric Reconstruction of Quantum Theory, I: The Abstract Quantum Formalism
• Ultimate data hiding in quantum mechanics and beyond
• Strong nonlocality: A trade-off between states and measurements
• Toolbox for reconstructing quantum theory from rules on information acquisition
• Deriving Grover's lower bound from simple physical principles
• Computation in generalised probabilistic theories
• Reconstructing quantum theory from diagrammatic postulates
• The computational landscape of general physical theories
• Thermodynamics and the structure of quantum theory
• On quantum vs. classical probability
• Three-dimensionality of space and the quantum bit: an information-theoretic approach
• Quantum theory from rules on information acquisition
• Conjugates, Filters and Quantum Mechanics
• Quantum computation is the unique reversible circuit model for which bits are balls
• Oracles and query lower bounds in generalised probabilistic theories
• An operational approach to spacetime symmetries: Lorentz transformations from quantum communication
• Information and communication in polygon theories
• Bounds on the power of proofs and advice in general physical theories
• How to make unforgeable money in generalised probabilistic theories
• Derivation of the Rules of Quantum Mechanics from Information-Theoretic Axioms
• Simple proof of the impossibility of bit-commitment in generalised probabilistic theories using cone programming
• An effect-theoretic reconstruction of quantum theory
• Interferometric computation beyond quantum theory
• The complex and quaternionic quantum bit from relativity of simultaneity on an interferometer
• Quantum information causality
• Measurement-based quantum foundations
• Hyperdense coding and superadditivity of classical capacities in hypersphere theories
• Reversible Dynamics in Strongly Non-Local Boxworld Systems
• On the impossibility of coin-flipping in generalized probabilistic theories via discretizations of semi-infinite programs
• Derivation of quantum theory with superselection rules