Introducing the Qplex: A Novel Arena for Quantum Theory

Abstract

We reconstruct quantum theory starting from the premise that, as Asher Peres remarked, "Unperformed experiments have no results." The tools of modern quantum information theory, and in particular the symmetric informationally complete (SIC) measurements, provide a concise expression of how exactly Peres's dictum holds true. That expression is a constraint on how the probability distributions for outcomes of different, mutually exclusive experiments mesh together, a type of constraint not foreseen in classical thinking. Taking this as our foundational principle, we show how to reconstruct the formalism of quantum theory in finite-dimensional Hilbert spaces. Along the way, we derive a condition for the existence of a d-dimensional SIC.

30 pages, 4 figures, 3 appendices; v2: typos and notational glitches corrected

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Cited by in corpus (39)

• The SIC Question: History and State of Play
• Notwithstanding Bohr, the Reasons for QBism
• Probabilistic Simulation of Quantum Circuits with the Transformer
• Symmetric Informationally Complete Measurements Identify the Irreducible Difference between Classical and Quantum Systems
• Universally Fisher-Symmetric Informationally Complete Measurements
• QBism: Quantum Theory as a Hero's Handbook
• Quantum theory from rules on information acquisition
• Variational autoencoder reconstruction of complex many-body physics
• Probability representation of quantum dynamics using pseudostochastic maps
• A structure theorem for generalized-noncontextual ontological models
• QBism Is Not So Simply Dismissed
• Discrete Wigner Functions from Informationally Complete Quantum Measurements
• Implementation of generalized measurements on a qudit via quantum walks
• Born's rule as a quantum extension of Bayesian coherence
• Lüders Channels and the Existence of Symmetric Informationally Complete Measurements
• Negativity Bounds for Weyl-Heisenberg Quasiprobability Representations
• Extending the Agent in QBism
• Quantum Theory is a Quasi-stochastic Process Theory
• Quantum Measurements in the Light of Quantum State Estimation
• Minimal informationally complete measurements for probability representation of quantum dynamics
• Quantum Bayesian Inference in Quasiprobability Representations
• Quantum Theory as Symmetry Broken by Vitality
• SICs: Some explanations
• Ideas Abandoned en Route to QBism
• Epistemic-Pragmatist Interpretations of Quantum Mechanics: A Comparative Assessment
• Is the SIC Outcome There When Nobody Looks?
• Bell non-locality using tensor networks and sparse recovery
• Quantum Reconstructions as Stepping Stones toward Psi-Doxastic Interpretations?
• Morphophoric POVMs, generalised qplexes, and 2-designs
• Misreading EPR: Variations on an Incorrect Theme
• Minimizing the negativity of quantum circuits in overcomplete quasiprobability representations
• Operational detection of entanglement via quantum designs
• Defending the Quantum Reconstruction Program
• On Relationalist Reconstructions of Quantum Theory
• A Theory of Inaccessible Information
• Can QBism exist without Q? Morphophoric measurements in generalised probabilistic theories
• Does Quantum Mechanics Breed Larger, More Intricate Quantum Theories? The Case for Experience-Centric Quantum Theory and the Interactome of Quantum Theories
• QBians Do Not Exist
• Quantum causal models via QBism