A derivation of quantum theory from physical requirements

Abstract

Quantum theory is usually formulated in terms of abstract mathematical postulates, involving Hilbert spaces, state vectors, and unitary operators. In this work, we show that the full formalism of quantum theory can instead be derived from five simple physical requirements, based on elementary assumptions about preparation, transformations and measurements. This is more similar to the usual formulation of special relativity, where two simple physical requirements -- the principles of relativity and light speed invariance -- are used to derive the mathematical structure of Minkowski space-time. Our derivation provides insights into the physical origin of the structure of quantum state spaces (including a group-theoretic explanation of the Bloch ball and its three-dimensionality), and it suggests several natural possibilities to construct consistent modifications of quantum theory.

16 pages, 2 figures. V3: added alternative formulation of Requirement 5, extended abstract, some minor modifications

References in corpus (6)

• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Information Causality as a Physical Principle
• Probabilistic theories with purification
• A practical scheme for quantum computation with any two-qubit entangling gate
• A glance beyond the quantum model
• All reversible dynamics in maximally non-local theories are trivial

Cited by in corpus (210)

• Quantum correlations with no causal order
• How Quantum Mechanics can consistently describe the use of itself
• Quantum theory cannot consistently describe the use of itself
• Almost quantum correlations
• Kochen-Specker Contextuality
• General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
• Generalized Probability Theories: What determines the structure of quantum theory?
• Tsirelson's problem and Kirchberg's conjecture
• A change of perspective: switching quantum reference frames via a perspective-neutral framework
• QBism and the Greeks: why a quantum state does not represent an element of physical reality
• Higher-order interference and single-system postulates characterizing quantum theory
• Existence of an information unit as a postulate of quantum theory
• Quantum theory from questions
• General probabilistic theories: An introduction
• On Formalisms and Interpretations
• Interpretations of quantum theory: A map of madness
• Generalized Probabilistic Theories Without the No-Restriction Hypothesis
• A free energy principle for generic quantum systems
• Degree of Complementarity Determines the Nonlocality in Quantum Mechanics
• An introduction to operational quantum dynamics
• A purification postulate for quantum mechanics with indefinite causal order
• The Operator Tensor Formulation of Quantum Theory
• A no-go theorem on the nature of the gravitational field beyond quantum theory
• Laws of Nature as Constraints
• No Return to Classical Reality
• Introducing the Qplex: A Novel Arena for Quantum Theory
• Deriving quantum theory from its local structure and reversibility
• Experimentally bounding deviations from quantum theory in the landscape of generalized probabilistic theories
• Density cubes and higher-order interference theories
• Operational quantum theory without predefined time
• Operational formulation of time reversal in quantum theory
• The exclusivity principle forbids sets of correlations larger than the quantum set
• Entanglement and thermodynamics in general probabilistic theories
• Quantum theory as the most robust description of reproducible experiments
• Quantum Theory, namely the pure and reversible theory of information
• Law without law: from observer states to physics via algorithmic information theory
• Understanding nature from experimental observations: a theory independent test for gravitational decoherence
• Experimental entanglement of temporal order
• Entanglement and superposition are equivalent concepts in any physical theory
• Toolbox for reconstructing quantum theory from rules on information acquisition
• If no information gain implies no disturbance, then any discrete physical theory is classical
• The arrow of time in operational formulations of quantum theory
• Dynamics of quantum causal structures
• How device-independent approaches change the meaning of physical theory
• Thermodynamics and the structure of quantum theory
• The computational landscape of general physical theories
• Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction
• Reconstructing quantum theory from diagrammatic postulates
• Classical Physics and the Bounds of Quantum Correlations
• Dilation of states and processes in operational-probabilistic theories
• Ruling out higher-order interference from purity principles
• Categorical Probabilistic Theories
• Three-dimensionality of space and the quantum bit: an information-theoretic approach
• Dimension of physical systems, information processing, and thermodynamics
• Closed sets of correlations: answers from the zoo
• Bridging the gap between general probabilistic theories and the device-independent framework for nonlocality and contextuality
• Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality
• Microcanonical thermodynamics in general physical theories
• Nonlocality Without Entanglement: Quantum Theory and Beyond
• Experimental observation of impossible-to-beat quantum advantage on a hybrid photonic system
• Hyperbits: the information quasiparticles
• Contextuality of general probabilistic theories
• Quantum theory from rules on information acquisition
• Internal quantum reference frames for finite Abelian groups
• Unifying typical entanglement and coin tossing: on randomization in probabilistic theories
• Composites and Categories of Euclidean Jordan Algebras
• Almost quantum correlations violate the no-restriction hypothesis
• Narratives of Quantum Theory in the Age of Quantum Technologies
• Conjugates, Filters and Quantum Mechanics
• Memory cost of temporal correlations
• Quantum computation is the unique reversible circuit model for which bits are balls
• Semi-definite programming and quantum information
• A general framework for phase and interference
• Positive maps and entanglement in real Hilbert spaces
• Information-theoretic postulates for quantum theory
• Observation of stronger-than-binary correlations with entangled photonic qutrits
• An operational approach to spacetime symmetries: Lorentz transformations from quantum communication
• Information-theoretic constraints on correlations with indefinite causal order
• Information and communication in polygon theories
• Entangled Histories vs. the Two-State-Vector Formalism - Towards a Better Understanding of Quantum Temporal Correlations
• Beyond the Cabello-Severini-Winter framework: Making sense of contextuality without sharpness of measurements
• General Bayesian theories and the emergence of the exclusivity principle
• Universal gaps for XOR games from estimates on tensor norm ratios
• Bipartite post-quantum steering in generalised scenarios
• Almost Quantum Correlations are Inconsistent with Specker's Principle
• Free quantum field theory from quantum cellular automata: derivation of Weyl, Dirac and Maxwell quantum cellular automata
• An effect-theoretic reconstruction of quantum theory
• A Gleason-type theorem for qubits based on mixtures of projective measurements
• Quantum resource covariance
• Communication of partial ignorance with qubits
• Mutually Unbiased Balanced Functions & Generalized Random Access Codes
• Experimentally bounding deviations from quantum theory for a photonic three-level system using theory-agnostic tomography
• Classification of all alternatives to the Born rule in terms of informational properties
• Quantum theory as plausible reasoning applied to data obtained by robust experiments
• Routed quantum circuits
• Any modification of the Born rule leads to a violation of the purification and local tomography principles
• How uncertainty enables non-classical dynamics
• Optimal processing of reversible quantum channels
• Operational Theories in Phase Space: Toy Model for the Harmonic Oscillator
• Interferometric computation beyond quantum theory
• Derivation of Quantum Theory from Feynman's Rules
• Reversibility and the structure of the local state space
• Agents, subsystems, and the conservation of information
• The complex and quaternionic quantum bit from relativity of simultaneity on an interferometer
• Perfect Discrimination of Non-Orthogonal Separable Pure States on Bipartite System in General Probabilistic Theory
• The Relativity Principle at the Foundation of Quantum Mechanics
• Quantum walks, deformed relativity, and Hopf algebra symmetries
• Information Content of Systems as a Physical Principle
• On defining the Hamiltonian beyond quantum theory
• Dense Coding with Locality Restriction for Decoder: Quantum Encoders vs. Super-Quantum Encoders
• General Probabilistic Theories with a Gleason-type Theorem
• Typical local measurements in generalised probabilistic theories: emergence of quantum bipartite correlations
• Quantum Process Identification: A Method for Characterizing Non-Markovian Quantum Dynamics
• The principle of information symmetry constrains the state-space in any physical theory
• Hyperdense coding and superadditivity of classical capacities in hypersphere theories
• Perfect Discrimination in Approximate Quantum Theory of General Probabilistic Theories
• Logical inference approach to relativistic quantum mechanics: derivation of the Klein-Gordon equation
• Advantage of Quantum Theory Over Non-classical Models of Communication
• Quantum mechanics is a calculus for estimation under epistemic restriction
• Reversible Dynamics in Strongly Non-Local Boxworld Systems
• Cellular automata in operational probabilistic theories
• Quaternionic quantum theory admits universal dynamics only for two-level systems
• Probabilistic Theories and Reconstructions of Quantum Theory (Les Houches 2019 lecture notes)
• Universal structure of objective states in all fundamental causal theories
• Quantum theory as a critical regime of language dynamics
• Nonlinear Schrödinger equations and generalized Heisenberg uncertainty principle violating the principle of estimation independence
• Separation of conditions as a prerequisite for quantum theory
• Symmetry and Self-Duality in Categories of Probabilistic Models
• Local Orthogonality provides better upper bound for Hardy's nonlocality
• Derivation of quantum theory with superselection rules
• Minimal Port-based Teleportation
• A simple and quantum-mechanically motivated characterization of the formally real Jordan algebras
• Quantum from principles without assuming definite causal structure
• Epistemic-Pragmatist Interpretations of Quantum Mechanics: A Comparative Assessment
• Gaussian distributions, Jacobi group and Siegel-Jacobi space
• How dynamics constrains probabilities in general probabilistic theories
• Von Neumann's information engine without the spectral theorem
• Interference as an information-theoretic game
• Assemblages and steering in general probabilistic theories
• Conservation of information and the foundations of quantum mechanics
• Data-Driven Inference, Reconstruction, and Observational Completeness of Quantum Devices
• Timelike correlations and quantum tensor product structure
• On affine maps on non-compact convex sets and some characterizations of finite-dimensional solid ellipsoids
• Generalized dynamical theories in phase space and the hydrogen atom
• Response to "The measurement postulates of quantum mechanics are not redundant"
• A classical formulation of quantum theory?
• Real or Not Real that is the question
• Estimation independence as an axiom for quantum uncertainty
• Quantum Darwinism and the spreading of classical information in non-classical theories
• Separability Criterion for Quantum Effects
• Spooky action at a distance in general probabilistic theories
• On the origin of nonclassicality in single systems
• Born's rule from almost nothing
• On characterising assemblages in Einstein-Podolsky-Rosen scenarios
• Quantum fluctuations from a local-causal information dynamics
• Shadows and subsystems of generalized probabilistic theories: when tomographic incompleteness is not a loophole for contextuality proofs
• Process tomography in general physical theories
• Scalar fermionic cellular automata on finite Cayley graphs
• A computer scientist's reconstruction of quantum theory
• A Royal Road to Quantum Theory (or Thereabouts), Extended Abstract
• Quantum Mechanics Based on an Extended Least Action Principle and Information Metrics of Vacuum Fluctuations
• The Operational Choi-Jamiolkowski Isomorphism
• Revisiting dynamics of quantum causal structures -- when can causal order evolve?
• Simulating all multipartite non-signalling channels via quasiprobabilistic mixtures of local channels in generalised probabilistic theories
• Multi-system measurements in generalized probabilistic theories and their role in information processing
• Quantum Scalar Field Theory Based on the Extended Least Action Principle
• Macroscopic locality with equal bias reproduces with high fidelity a quantum distribution achieving the Tsirelson's bound
• Quantum dynamics and kinematics from a statistical model selected by the principle of Locality
• The problem of quantum correlations and the totalitarian principle
• Generalized Probabilistic Description of Noninteracting Identical Particles
• The incompatibility of quantum channels in general probabilistic theories
• The operational framework for quantum theories is both epistemologically and ontologically neutral
• What is \textit{Quantum} in Probabilistic Explanations of the Sure Thing Principle Violation?
• Is the local linearity of space-time inherited from the linearity of probabilities?
• Algorithmic idealism: what should you believe to experience next?
• Local tomography and the role of the complex numbers in quantum mechanics
• Theory-independent randomness generation from spatial symmetries
• Reflections on Zeilinger-Brukner information interpretation of quantum mechanics
• Non-locality in theories without the no-restriction hypothesis
• Reconstruction of Quantum Particle Statistics: Bosons, Fermions, and Transtatistics
• Shannon theory for quantum systems and beyond: information compression for fermions
• Quantum field theory from first principles
• An attempt to understand relational quantum mechanics
• Universality of Computation in Real Quantum Theory
• Quantum correlations cannot be reproduced with a finite number of measurements in any no-signaling theory
• Expanding the principle of local distinguishability
• Complete extension: the non-signaling analog of quantum purification
• Multi-object operational tasks for measurement incompatibility
• A stochastic model for quantum measurement
• Unexpected consequences of Post-Quantum theories in the graph-theoretical approach to correlations
• Optimal CHSH values for regular polygon theories in generalized probabilistic theories
• Theory-independent monitoring of the decoherence of a superconducting qubit with generalized contextuality
• Remarks on the tensor product structure of no-signaling theories
• Symmetries and Wigner representations of operational theories
• Maximum Dimension of Subspaces with No Product Basis
• Programming of channels in generalized probabilistic theories
• Are almost-symmetries almost linear?
• Minimal operational theories: classical theories with quantum features
• Spin Theory Based on the Extended Least Action Principle and Information Metrics: Quantization, Entanglement, and Bell Test With Time Delay
• Information-theoretic derivation of energy, speed bounds, and quantum theory
• Intermediate determinism in general probabilistic theories
• Ruling out the class of statistical processes involving two noninteracting identical particles in two modes
• Does Quantum Mechanics Breed Larger, More Intricate Quantum Theories? The Case for Experience-Centric Quantum Theory and the Interactome of Quantum Theories
• The operational foundations of PT-symmetric and quasi-Hermitian quantum theory
• Gleason's Theorem for a Qubit as Part of a Composite System
• Towards establishing a connection between two-level quantum systems and physical spaces
• Uncertainty principle certifies genuine source of intrinsic randomness
• Conjugate Logic
• The relativistic reason for quantum probability amplitudes
• Spacetime symmetries and the qubit Bloch ball: a physical derivation of finite dimensional quantum theory and the number of spatial dimensions