Quantum Theory as Symmetry Broken by Vitality

Abstract

I summarize a research program that aims to reconstruct quantum theory from a fundamental physical principle that, while a quantum system has no intrinsic hidden variables, it can be understood using a reference measurement. This program reduces the physical question of why the quantum formalism is empirically successful to the mathematical question of why complete sets of equiangular lines appear to exist in complex vector spaces when they do not exist in real ones. My primary goal is to clarify motivations, rather than to present a closed book of numbered theorems, and consequently the discussion is more in the manner of a colloquium than a PRL.

32 pages, 1 figure; the tone and topic of a Chris Fuchs samizdat, but 1/100th the size; v6: new discussion of spectral property, section 5 streamlined

References in corpus (35)

• Symmetric Informationally Complete Quantum Measurements
• In defense of the epistemic view of quantum states: a toy theory
• Quantum-Bayesian Coherence: The No-Nonsense Version
• The sphere packing problem in dimension 24
• SIC-POVMs: A new computer study
• The SIC Question: History and State of Play
• Jarzynski-like equality for the out-of-time-ordered correlator
• Limited Holism and Real-Vector-Space Quantum Theory
• Equiangular lines in Euclidean spaces
• Typical Physics PhD Admissions Criteria Limit Access to Underrepresented Groups but Fail to Predict Doctoral Completion, including some additional information
• SIC~POVMs and Clifford groups in prime dimensions
• Real-Vector-Space Quantum Theory with a Universal Quantum Bit
• A Kochen-Specker inequality from a SIC
• Optimal simplices and codes in projective spaces
• Introducing the Qplex: A Novel Arena for Quantum Theory
• Making better sense of quantum mechanics
• Quasiprobability representations of quantum mechanics with minimal negativity
• Symmetric Informationally Complete Measurements Identify the Irreducible Difference between Classical and Quantum Systems
• SICs: Extending the list of solutions
• Bargmann invariants and off-diagonal geometric phases for multi-level quantum systems -- a unitary group approach
• Informational power of the Hoggar SIC-POVM
• Von Neumann Was Not a Quantum Bayesian
• Structure of Two-qubit Symmetric Informationally Complete POVMs
• SIC-POVMs and Compatibility among Quantum States
• Sporadic SICs and the Normed Division Algebras
• Dimension towers of SICs. I. Aligned SICs and embedded tight frames
• Priors in quantum Bayesian inference
• Multiscale Structure in Eco-Evolutionary Dynamics
• Geometric and Information-Theoretic Properties of the Hoggar Lines
• Strongly symmetric spectral convex bodies are Jordan algebra state spaces
• Misreading EPR: Variations on an Incorrect Theme
• From Einstein's 1905 Postulates to the Geometry of Flat Space-Time
• Invariant Off-Diagonality: SICs as Equicoherent Quantum States
• QBism and the Ithaca Desiderata
• Multiscale Structure of More-than-Binary Variables

Cited by in corpus (7)

• Negative quasiprobabilities enhance phase estimation in quantum-optics experiment
• QBism and Relational Quantum Mechanics compared
• Born's rule as a quantum extension of Bayesian coherence
• Lüders Channels and the Existence of Symmetric Informationally Complete Measurements
• Ideas Abandoned en Route to QBism
• On Two Recent Approaches to the Born Rule
• QBians Do Not Exist