Generalized Probability Theories: What determines the structure of quantum theory?

Abstract

The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical structure of quantum theory. This review paper tries to present the framework and recent results to a broader readership in an accessible manner. To achieve this, we follow a constructive approach. Starting from few basic physically motivated assumptions we show how a given set of observations can be manifested in an operational theory. Furthermore, we characterize consistency conditions limiting the range of possible extensions. In this framework classical and quantum theory appear as special cases, and the aim is to understand what distinguishes quantum mechanics as the fundamental theory realized in nature. It turns out non-classical features of single systems can equivalently result from higher dimensional classical theories that have been restricted. Entanglement and non-locality, however, are shown to be genuine non-classical features.

39 pages, 12 figures

References in corpus (17)

• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Bounding the set of quantum correlations
• The uncertainty principle determines the non-locality of quantum mechanics
• A derivation of quantum theory from physical requirements
• A generalized no-broadcasting theorem
• Non-locality distillation and post-quantum theories with trivial communication complexity
• Recovering part of the quantum boundary from information causality
• Existence of an information unit as a postulate of quantum theory
• Generalized Probabilistic Theories Without the No-Restriction Hypothesis
• Non-disturbing quantum measurements
• Implausible Consequences of Superstrong Nonlocality
• Why Physics Needs Quantum Foundations
• If no information gain implies no disturbance, then any discrete physical theory is classical
• Coexistence does not imply joint measurability
• Conjugates, Filters and Quantum Mechanics
• A general framework for phase and interference
• Non-locality in theories without the no-restriction hypothesis

Cited by in corpus (96)

• Equivalence of quantum barren plateaus to cost concentration and narrow gorges
• The Inflation Technique for Causal Inference with Latent Variables
• Higher-order interference and single-system postulates characterizing quantum theory
• A Comprehensive Review of Quantum Random Number Generators: Concepts, Classification and the Origin of Randomness
• Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes
• Quantum Theory and Determinism
• Experimentally bounding deviations from quantum theory in the landscape of generalized probabilistic theories
• What is nonclassical about uncertainty relations?
• Thermodynamics and the structure of quantum theory
• Measurement incompatibility and Schrödinger-EPR steering in a class of probabilistic theories
• Incompatible measurements in a class of general probabilistic theories
• Contextuality of general probabilistic theories
• Classical theories with entanglement
• Any consistent coupling between classical gravity and quantum matter is fundamentally irreversible
• Semi-definite programming and quantum information
• Structure of Optimal State Discrimination in Generalized Probabilistic Theories
• Classicality without local discriminability: decoupling entanglement and complementarity
• Tunnelling necessitates negative Wigner function
• Experimentally bounding deviations from quantum theory for a photonic three-level system using theory-agnostic tomography
• Solvable Criterion for the Contextuality of any Prepare-and-Measure Scenario
• An Algebraic Approach to Koopman Classical Mechanics
• A healthier semi-classical dynamics
• Contextuality with vanishing coherence and maximal robustness to dephasing
• Dense Coding with Locality Restriction for Decoder: Quantum Encoders vs. Super-Quantum Encoders
• Operational foundations of complementarity and uncertainty relations
• On defining the Hamiltonian beyond quantum theory
• Memory Effects in Quantum Processes
• General Probabilistic Theories with a Gleason-type Theorem
• The future of secure communications: device independence in quantum key distribution
• The principle of information symmetry constrains the state-space in any physical theory
• Perfect Discrimination in Approximate Quantum Theory of General Probabilistic Theories
• Advantage of Quantum Theory Over Non-classical Models of Communication
• A Survey of Physical Principles Attempting to Define Quantum Mechanics
• Probabilistic Theories and Reconstructions of Quantum Theory (Les Houches 2019 lecture notes)
• Universal structure of objective states in all fundamental causal theories
• Bell measurement rules out supraquantum correlations
• Preparation Uncertainty Implies Measurement Uncertainty in a Class of Generalized Probabilistic Theories
• Asymptotic Properties for Markovian Dynamics in Quantum Theory and General Probabilistic Theories
• Pseudo standard entanglement structure cannot be distinguished from standard entanglement structure
• Unification of energy concepts in generalised phase space theories
• Von Neumann's information engine without the spectral theorem
• Compact convex structure of measurements and its applications to simulability, incompatibility, and convex resource theory of continuous-outcome measurements
• From reasonable postulates to generalised Hamiltonian systems
• Generalized dynamical theories in phase space and the hydrogen atom
• Nonlinear Bell inequality for macroscopic measurements
• Entropy of mixing exists only for classical and quantum-like theories among the regular polygon theories
• The collapse of a quantum state as a joint probability construction
• Quantum Darwinism and the spreading of classical information in non-classical theories
• On the origin of nonclassicality in single systems
• Separability Criterion for Quantum Effects
• From the problem of Future Contingents to Peres-Mermin square experiments: An introductory review to Contextuality
• Advantages of quantum communication revealed by the reexamination of hyperbit theory limitations
• Hierarchical axioms for quantum mechanics
• Classical Limits and Contextuality in a Scenario of Multiple Observers
• Robustness of contextuality under different types of noise as quantifiers for parity-oblivious multiplexing tasks
• Constrained Measurement Incompatibility from Generalised Contextuality of Steered Preparation
• Entropic Uncertainty Relations in a Class of Generalized Probabilistic Theories
• The violation of Bell-CHSH inequalities leads to different conclusions depending on the description used
• Wigner and friends, a map is not the territory! Contextuality in multi-agent paradoxes
• The incompatibility of quantum channels in general probabilistic theories
• Quantum Advantage: A Single Qubit's Experimental Edge in Classical Data Storage
• The operational framework for quantum theories is both epistemologically and ontologically neutral
• The operational reality of quantum nonlocality
• On the notion of composite system
• No Disturbance Without Uncertainty as a Physical Principle
• Emergence of noncontextuality under quantum Darwinism
• Entanglement-breaking channels with general outcome operator algebras
• Symmetry-induced failures of tomographic locality: Constructing foil theories by twirling
• Beyond the Projection Postulate and Back: Quantum Theories with Generalised State-Update Rules
• A simple formulation of no-cloning and no-hiding that admits efficient and robust verification
• Structure of quantum and classical implementations of Popescu-Rohrlich box
• Holographic Transformation, Belief Propagation and Loop Calculus for Generalized Probabilistic Theories
• Intersubjectivity and value reproducibility of outcomes of quantum measurements
• Symmetric observations without symmetric causal explanations
• Comment on 'The operational foundations of PT-symmetric and quasi-Hermitian quantum theory'
• Theory-independent monitoring of the decoherence of a superconducting qubit with generalized contextuality
• Uncertainty-Complementarity Balance as a General Constraint on Non-locality
• Time Symmetric Quantum Theory Without Retrocausality? A Reply to Tim Maudlin
• Symmetries and Wigner representations of operational theories
• Maximum Dimension of Subspaces with No Product Basis
• Causal nonseparability and its implications for spatiotemporal relations
• Constraints on a Generalization of Geometric Quantum Mechanics from Neutrino and $B^0$-$\overline{B^0}$ Oscillations
• Decoupling local classicality from classical explainability: A noncontextual model for bilocal classical theory and a locally-classical but contextual theory
• Infinite dimensionality of the post-processing order of measurements on a general state space
• Differential Geometry of Contextuality
• Generalising Aumann's Agreement Theorem
• Intermediate determinism in general probabilistic theories
• Gleason's Theorem for a Qubit as Part of a Composite System
• Bipartite polygon models: entanglement classes and their nonlocal behaviour
• Randomness-free Detection of Non-projective Measurements: Qubits & beyond
• One-shot and asymptotic classical capacity in general physical theories
• The operational foundations of PT-symmetric and quasi-Hermitian quantum theory
• Typicality of Contextuality
• Operational nonlocality
• Ruling out the class of statistical processes involving two noninteracting identical particles in two modes
• Quantum interpretations, causality and quantum computation