SciPost Physics Lecture Notes

SciPost Phys. Lect. Notes 28 (2021) · published 31 March 2021

Part of the 2019-07: Quantum Information Machines Collection in the Les Houches Summer School Lecture Notes Series.

• doi: 10.21468/SciPostPhysLectNotes.28
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

Abstract

These lecture notes provide a basic introduction to the framework of generalized probabilistic theories (GPTs) and a sketch of a reconstruction of quantum theory (QT) from simple operational principles. To build some intuition for how physics could be even more general than quantum, I present two conceivable phenomena beyond QT: superstrong nonlocality and higher-order interference. Then I introduce the framework of GPTs, generalizing both quantum and classical probability theory. Finally, I summarize a reconstruction of QT from the principles of Tomographic Locality, Continuous Reversibility, and the Subspace Axiom. In particular, I show why a quantum bit is described by a Bloch ball, why it is three-dimensional, and how one obtains the complex numbers and operators of the usual representation of QT.

• Plávala, Incompatibility in restricted operational theories: connecting contextuality and steering
  J. Phys. A: Math. Theor. 55, 174001 (2022) [Crossref]
• Galley et al., A no-go theorem on the nature of the gravitational field beyond quantum theory
  Quantum 6, 779 779 (2022) [Crossref]
• Heinosaari et al., Dispensing of quantum information beyond no-broadcasting theorem—is it possible to broadcast anything genuinely quantum?
  J. Phys. A: Math. Theor. 56, 135301 (2023) [Crossref]
• Stuckey et al., No Preferred Reference Frame at the Foundation of Quantum Mechanics
  Entropy 24, 12 (2021) [Crossref]
• Minagawa et al., One-shot and asymptotic classical capacity in general physical theories
  Phys. Rev. A 109, 062416 (2024) [Crossref]
• Höhn et al., Internal quantum reference frames for finite Abelian groups
  63, 112207 (2022) [Crossref]
• Müller et al., Testing Quantum Theory by Generalizing Noncontextuality
  Phys. Rev. X 13, 041001 (2023) [Crossref]
• [undetermined], Survey the foundations
  Nat. Phys. 18, 961 (2022) [Crossref]
• Aubrun et al., Entanglement and Superposition Are Equivalent Concepts in Any Physical Theory
  Phys. Rev. Lett. 128, 160402 (2022) [Crossref]
• Ali Ahmad et al., Quantum Relativity of Subsystems
  Phys. Rev. Lett. 128, 170401 (2022) [Crossref]
• Di Biagio, Diagrams and GPTs for Quantum Gravity
  Quantum Views 8, 78 78 (2024) [Crossref]
• Selby et al., Linear Program for Testing Nonclassicality and an Open-Source Implementation
  Phys. Rev. Lett. 132, 050202 (2024) [Crossref]
• Cavalcanti et al., Every nonsignaling channel is common-cause realizable
  Phys. Rev. A 109, 042211 (2024) [Crossref]
• Lami et al., A post-quantum associative memory
  J. Phys. A: Math. Theor. 56, 455304 (2023) [Crossref]
• Winczewski et al., Complete extension: the non-signaling analog of quantum purification
  Quantum 7, 1159 1159 (2023) [Crossref]
• Adlam, Operational theories as structural realism
  Studies in History and Philosophy of Science 94, 99 (2022) [Crossref]
• Plávala et al., Generalized dynamical theories in phase space and the hydrogen atom
  Phys. Rev. A 108, 052212 (2023) [Crossref]
• Giordani et al., Experimental certification of contextuality, coherence, and dimension in a programmable universal photonic processor
  Sci. Adv. 9, eadj4249 (2023) [Crossref]
• Baldijao et al., Quantum Darwinism and the spreading of classical information in non-classical theories
  Quantum 6, 636 636 (2022) [Crossref]
• Cavalcanti et al., Decomposing all multipartite non-signalling channels via quasiprobabilistic mixtures of local channels in generalised probabilistic theories
  J. Phys. A: Math. Theor. 55, 404001 (2022) [Crossref]
• Plávala et al., Operational Theories in Phase Space: Toy Model for the Harmonic Oscillator
  Phys. Rev. Lett. 128, 040405 (2022) [Crossref]