Probabilistic Theories and Reconstructions of Quantum Theory (Les Houches 2019 lecture notes)
arXiv:2011.01286 · doi:10.21468/SciPostPhysLectNotes.28
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.
arXiv comment41 pages, 12 figures. V2: added hyperlinks to references; several minor corrections; new layout. V3, V4: corrected some typos and added some minor clarifications. Submitted to SciPost Lecture Notes. To appear in 'Quantum Information Machines; Lecture Notes of the Les Houches Summer School 2019', eds. M. Devoret, B. Huard, and I. Pop
References in corpus (52)
- Significant-loophole-free test of Bell's theorem with entangled photons
- Random Numbers Certified by Bell's Theorem
- Relational Quantum Mechanics
- Models of Wave-function Collapse, Underlying Theories, and Experimental Tests
- No Signalling and Quantum Key Distribution
- Information Causality as a Physical Principle
- Quantum correlations with no causal order
- In defense of the epistemic view of quantum states: a toy theory
- Informational derivation of Quantum Theory
- Quantum Theory From Five Reasonable Axioms
- Probabilistic theories with purification
- Quantum Mechanics as Quantum Measure Theory
- Quantum Mechanics as Quantum Information (and only a little more)
- The lesson of causal discovery algorithms for quantum correlations: Causal explanations of Bell-inequality violations require fine-tuning
- Private Randomness Expansion With Untrusted Devices
- Characterizing quantum theory in terms of information-theoretic constraints
- A derivation of quantum theory from physical requirements
- A generalized no-broadcasting theorem
- Ruling Out Multi-Order Interference in Quantum Mechanics
- A glance beyond the quantum model
- Almost quantum correlations
- Local Quantum Measurement and No-Signaling Imply Quantum Correlations
- Generalized Probability Theories: What determines the structure of quantum theory?
- The no-signaling condition and quantum dynamics
- Higher-order interference and single-system postulates characterizing quantum theory
- Reformulating and Reconstructing Quantum Theory
- Quantum theory from questions
- All reversible dynamics in maximally non-local theories are trivial
- Limits on non-local correlations from the structure of the local state space
- The structure of reversible computation determines the self-duality of quantum theory
- Generalized Probabilistic Theories Without the No-Restriction Hypothesis
- Three Slit Experiments and the Structure of Quantum Theory
- Deriving quantum theory from its local structure and reversibility
- Density cubes and higher-order interference theories
- Obtaining tight bounds on higher-order interferences with a 5-path interferometer
- Law without law: from observer states to physics via algorithmic information theory
- Tsirelson's Problem
- Toolbox for reconstructing quantum theory from rules on information acquisition
- Geometry of the set of mixed quantum states: An apophatic approach
- Three-dimensionality of space and the quantum bit: an information-theoretic approach
- Bridging the gap between general probabilistic theories and the device-independent framework for nonlocality and contextuality
- Measurement sharpness cuts nonlocality and contextuality in every physical theory
- Quantum theory from rules on information acquisition
- Composites and Categories of Euclidean Jordan Algebras
- Quantum computation is the unique reversible circuit model for which bits are balls
- Quantum theory as a principle theory: insights from an information-theoretic reconstruction
- General Bayesian theories and the emergence of the exclusivity principle
- Sequences of projective measurements in generalized probabilistic models
- The complex and quaternionic quantum bit from relativity of simultaneity on an interferometer
- Strongly symmetric spectral convex bodies are Jordan algebra state spaces
- A Royal Road to Quantum Theory (or Thereabouts), Extended Abstract
- Semi-device-independent information processing with spatiotemporal degrees of freedom