Quantum Theory of Probability and Decisions

Abstract

The probabilistic predictions of quantum theory are conventionally obtained from a special probabilistic axiom. But that is unnecessary because all the practical consequences of such predictions follow from the remaining, non-probabilistic, axioms of quantum theory, together with the non-probabilistic part of classical decision theory.

Cited by in corpus (168)

• Decoherence, einselection, and the quantum origins of the classical
• Decoherence, the measurement problem, and interpretations of quantum mechanics
• Multi-Player Quantum Games
• Probabilities from Entanglement, Born's Rule from Envariance
• Information Flow in Entangled Quantum Systems
• Dynamical Origin of Quantum Probabilities
• Quantum Market Games
• Constructor Theory of Information
• Self-Locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics
• Playing a quantum game with a corrupted source
• Probability in the Everett World: Comments on Wallace and Greaves
• On Formalisms and Interpretations
• Physics of risk and uncertainty in quantum decision making
• Quantum Probability from Decision Theory?
• The Born Rule in Quantum and Classical Mechanics
• On Zurek's derivation of the Born rule
• Experimental motivation and empirical consistency in minimal no-collapse quantum mechanics
• Quantum Theory and Determinism
• Many-Worlds and Schroedinger's First Quantum Theory
• Quantum Theory of the Classical: Einselection, Envariance, Quantum Darwinism and Extantons
• Dimensional Transmutation in Gravity and Cosmology
• Quantum Theory of the Classical: Quantum Jumps, Born's Rule, and Objective Classical Reality via Quantum Darwinism
• The measurement postulates of quantum mechanics are operationally redundant
• The Quantum Measurement Problem: State of Play
• Quantum Mechanics as Classical Physics
• Interpreting Quantum Particles as Conceptual Entities
• Quantum Probabilities as Behavioral Probabilities
• The Born Rule Dies
• How unitary cosmology generalizes thermodynamics and solves the inflationary entropy problem
• Is Quantum Mechanics An Island In Theoryspace?
• Origin of probabilities and their application to the multiverse
• A formal proof of the Born rule from decision-theoretic assumptions
• The EPR paradox, Bell's inequality, and the question of locality
• Quantum Probability and Decision Theory, Revisited
• Discreteness and the origin of probability in quantum mechanics
• Projective Expected Utility
• The Problem of Confirmation in the Everett Interpretation
• Branch-counting in the Everett Interpretation of quantum mechanics
• An introduction to many worlds in quantum computation
• Causation, decision theory, and Bell's theorem: a quantum analogue of the Newcomb problem
• Broken Time Translation Symmetry as a model for Quantum State Reduction
• Many-particle interference to test Born's rule
• Why the Many-Worlds Interpretation?
• Limits on Efficient Computation in the Physical World
• A Nanoscale Experiment Measuring Gravity's Role in Breaking the Unitarity of Quantum Dynamics
• Vortex interaction, chaos and quantum probabilities
• Many-Measurements or Many-Worlds? A Dialogue
• Real World Interpretations of Quantum Theory
• Everettian probabilities, the Deutsch-Wallace theorem and the Principal Principle
• Classification of all alternatives to the Born rule in terms of informational properties
• When Worlds Collide: Quantum Probability From Observer Selection?
• Constructor Theory of Probability
• Meaning of the wave function
• Any modification of the Born rule leads to a violation of the purification and local tomography principles
• Quantum Probability from Subjective Likelihood: improving on Deutsch's proof of the probability rule
• Quantum Mechanics from Focusing and Symmetry
• Probability amplitude in quantum like games
• Extended statistical modeling under symmetry; the link toward quantum mechanics
• Weak Values as Context Dependent Values of Observables and Born's Rule
• Complex and Unpredictable Cardano
• On unitary evolution and collapse in Quantum Mechanics
• Many Worlds, the Born Rule, and Self-Locating Uncertainty
• Born Rule and Noncontextual Probability
• Quantum mechanics is a calculus for estimation under epistemic restriction
• Quantum Structures of a Model-Universe: An Inconsistency with Everett Interpretation of Quantum Mechanics
• Pulsed and continuous measurements of exponentially decaying systems
• Quantum mechanics as a deterministic theory of a continuum of worlds
• On the problem of the interpretation of quantum physics
• What is Probability?
• Why Current Interpretations of Quantum Mechanics are Deficient
• Emergence of the Born rule in quantum optics
• Inter-Theory Relations in Physics: Case Studies from Quantum Mechanics and Quantum Field Theory
• No Evidence for Particles
• Quantum fractionalism: the Born rule as a consequence of the complex Pythagorean theorem
• Analysis of Wallace's Proof of the Born Rule in Everettian Quantum Mechanics II: Concepts and Axioms
• Making sense of Born's rule $p_{\alpha }=\Vert {\Psi }_{\alpha }{\Vert }^2$ with the many-minds interpretation
• The Relation between Wavefunction and 3D Space Implies Many Worlds with Local Beables and Probabilities
• Born rule: quantum probability as classical probability
• Probability in many-worlds theories
• Consistent theory for causal non-locality beyond Born's rule
• Derivation of quantum probabilities from deterministic evolution
• Everett and Structure
• Emergent Quantum Mechanics at the Boundary of a Local Classical Lattice Model
• Quantum theory as a statistical theory under symmetry and complementarity
• The Minimal Modal Interpretation of Quantum Theory
• A Subjective Approach to Quantum Probability
• An Elementary Proof That Everett's Quantum Multiverse Is Nonlocal: Bell-Locality and Branch-Symmetry in the Many-Worlds Interpretation
• Born's rule from almost nothing
• Group Representational Clues to a Theory Underlying Quantum Mechanics
• Analysis of Wallace's Proof of the Born Rule in Everettian Quantum Mechanics: Formal Aspects
• On the Everett programme and the Born rule
• Combining Bohm and Everett: Axiomatics for a Standalone Quantum Mechanics
• Quantum and classical probability as Bayes-optimal observation
• Decision theory and information propagation in quantum physics
• Everettian Rationality: defending Deutsch's approach to probability in the Everett interpretation
• The problem of quantum correlations and the totalitarian principle
• The Born rule
• $\Psi$-Epistemic Quantum Cosmology?
• On the ongoing experiments looking for higher-order interference: What are they really testing?
• Quasiprobability distributions with weak measurements
• Everettian theory as pure wave mechanics plus a no-collapse probability postulate
• Everett's Missing Postulate and the Born Rule
• Drift-Diffusion in Mangled Worlds Quantum Mechanics
• Problems with Probability in Everett's Interpretation of Quantum Mechanics
• Origin of time and probability in quantum cosmology
• Derivation of the quantum probability law from minimal non-demolition measurement
• Derivation of the Born Rule from Operational Assumptions
• Beyond Purity and Mixtures in Categorical Quantum Mechanics
• Environment-assisted invariance does not necessitate Born's rule for quantum measurement
• Towards a theory of wavefunction collapse Part 1: How the Diosi-Penrose criterion and Born's rule can be derived from semiclassical gravity, and how the criterion can be relativistically generalised with help of the Einstein-Hilbert action
• Everett's Multiverse and the World as Wavefunction
• On the Nature of $a_k^{\ast }{a}_k$ and the Emergence of the Born's Rule
• Has the Born rule been proven?
• The Cosmic Void
• Probability in modal interpretations of quantum mechanics
• Decoherence and Probability
• Kolmogorov's aporia and solution by construction of a relativized and quantified concept of factual probability
• Positive Operation Valued Measurement Based Multi-User Detection in DS-CDMA Systems
• Derivation of the Born rule from the unitarity of quantum evolution
• Probability in two deterministic universes
• Experimental Demonstration on Quantum Sensitivity to Available Information in Decision Making
• A non-probabilistic substitute for the Born rule
• Collapse of the many-worlds interpretation: Why Everett's theory is typically wrong
• Decoherence, Branching, and the Born Rule in a Mixed-State Everettian Multiverse
• Quantum theories with local information flow
• Probability, Preclusion and Biological Evolution in Heisenberg-Picture Everett Quantum Mechanics
• Quantum Immortality and Non-Classical Logic
• Derive the Born's rule from environment-induced stochastic dynamics of wave-functions in an open system
• Commentary on Quantum-Inspired Information Retrieval
• Quantum Probability as an Application of Data Compression Principles
• Interpretation Neutrality in the Classical Domain of Quantum Theory
• The Born Rule and Time-Reversal Symmetry of Quantum Equations of Motion
• Modelling an observer's branch of extremal consciousness
• The Many-Worlds Interpretation of Quantum Mechanics is Fatally Flawed
• Quantum Computing in the de Broglie-Bohm Pilot-Wave Picture
• Many Worlds Model resolving the Einstein Podolsky Rosen paradox via a Direct Realism to Modal Realism Transition that preserves Einstein Locality
• Investigations in quantum games using EPR-type set-ups
• Relative Frequency and Probability in the Everett Interpretation of Heisenberg-Picture Quantum Mechanics
• Quantum Computation Based Probability Density Function Estimation
• Reality is both digital and analog
• Dealing with ignorance: universal discrimination, learning and quantum correlations
• Structural Instability and Quantum Lying in the Many-worlds (Relative State) Interpretation
• Problems with information theoretic approaches to causal learning
• Everett and the Born Rule
• Against Absolute Actualization: Three "Non-Localities" and Failure of Model-External Randomness made easy with Many-Worlds Models including Stronger Bell-Violation and Correct QM Probability
• Toy observer in unitary evolution: Histories, consciousness, and state reduction
• The Dutch's Real World Financial Institute: Introducing Quantum-Like Bayesian Networks as an Alternative Model to deal with Uncertainty
• Dynamic consistency of expected utility under non-classical (quantum) uncertainty
• Quantum Probability: a reliable tool for an agent or a reliable source of reality?
• The Grammar of Teleportation
• General principles in the interpretation of quantum mechanics
• Are there really many worlds in the "Many-worlds interpretation" of Quantum Mechanics?
• Quantum Reasoning using Lie Algebra for Everyday Life (and AI perhaps...)
• Growth of Knowledge and Entropy in Quantum Physics
• A microscopic derivation of the quantum measurement postulates
• Quantum Computing, Postselection, and Probabilistic Polynomial-Time
• The inconsistency of linear dynamics and Born's rule
• Reverse quantum speed limit and minimum Hilbert space norm
• Relative descriptors for quantum agents
• Towards a test of the Born rule in high-energy collisions
• Quantum information processing, operational quantum logic, convexity, and the foundations of physics
• Observations of wavefunction collapse and the retrospective application of the Born rule
• On an Argument of David Deutsch
• Understanding Deutsch's probability in a deterministic multiverse
• Maximum Likelihood Based Quantum Set Separation
• Constraints on Interpretations of Quantum Mechanics
• Derivation of the probability law in the many-worlds, one-MIND interpretation
• Explanation, Evolution and Subjective Probability in Everett Quantum Mechanics with Positive Preclusion