# Derivation of the Born rule from operational assumptions

@article{Saunders2004DerivationOT, title={Derivation of the Born rule from operational assumptions}, author={Simon Saunders}, journal={Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences}, year={2004}, volume={460}, pages={1771 - 1788} }

The Born rule is derived from operational assumptions, together with assumptions of quantum mechanics that concern only the deterministic development of the state. Unlike Gleason's theorem, the argument applies even if probabilities are defined for only a single resolution of the identity, so it applies to a variety of foundational approaches to quantum mechanics. It also provides a probability rule for state spaces that are not Hilbert spaces.

## 110 Citations

Derivations of the Born Rule

- PhilosophyJerusalem Studies in Philosophy and History of Science
- 2020

The Born rule, a cornerstone of quantum theory usually taken as a postulate, continues to attract numerous attempts for its derivation. A critical review of these derivations, from early attempts to…

Chapter 26 Derivations of the Born Rule

- Philosophy
- 2020

The Born rule, a cornerstone of quantum theory usually taken as a postulate, continues to attract numerous attempts for its derivation. A critical review of these derivations, from early attempts to…

Born Rule and its Interpretation

- PhysicsCompendium of Quantum Physics
- 2009

The Born rule provides a link between the mathematical formalism of quantum theory and experiment, and as such is almost single-handedly responsible for practically all predictions of quantum…

A simple derivation of Born's rule with and without Gleason's theorem

- Physics
- 2015

We present a derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. Combined to Gleason's theorem,…

The Born rule

- Mathematics
- 2019

We deduce the Born rule. No use is required of quantum postulates. One exploits only rudimentary quantum mathematics -- a linear, not Hilbert's, vector space -- and empirical notion of the…

Learning using the Born Rule

- Computer Science
- 2006

A new probabilistic justification for popular algebraic algorithms, based on the Born rule, is unraveled, which includes two-class and multiple-class spectral clustering, and algorithms based on Euclidean distances.

Born Rule and Noncontextual Probability

- Mathematics
- 2012

We present a new derivation of the Born rule from the assumption of noncontextual probability (NCP). Within the theorem we also demonstrate the continuity of probability with respect to the…

Rescuing the Born Rule for Quantum Cosmology

- Mathematics
- 2011

Page has recently argued that the Born rule does not suffice for computing all probabilities in quantum cosmology. He further asserts that the Born rule's failure gives rise to the cosmological…

The Born rule as a statistics of quantum micro-events

- PhysicsProceedings of the Royal Society A
- 2020

We deduce the Born rule from a purely statistical take on quantum theory within minimalistic math-setup. No use is required of quantum postulates. One exploits only rudimentary quantum mathematics—a…

Macroscopic observables and the Born rule

- Mathematics
- 2008

We clarify the role of the Born rule in the Copenhagen Interpretation of quantum mechanics by deriving it from Bohr's doctrine of classical concepts, translated into the following mathematical…

## References

SHOWING 1-10 OF 24 REFERENCES

Quantum probability from decision theory?

- PhilosophyProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- 2000

In a recent paper, Deutsch claims to derive the ‘probabilistic predictions of quantum theory’ from the ‘non–probabilistic axioms of quantum theory’ and the ‘nonprobabilistic part of classical…

Quantum theory of probability and decisions

- Philosophy, PhysicsProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- 1999

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…

Hidden Variables, Statistical Mechanics and the Early Universe

- Physics
- 2001

One of the central mysteries of quantum theory is that it seems to be fundamentally nonlocal—and yet the nonlocality cannot be used for practical signalling at a distance. The consistency of modern…

Quantum mechanics of history: The decoherence functional in quantum mechanics.

- PhysicsPhysical review. D, Particles and fields
- 1992

A condition for approximate decoherence is proposed, and it is argued that most probability sum rules will be satisfied to approximately the same degree, and an inequality bounding the size of the off-diagonal terms of thedecoherence functional is derived.

Everettian Rationality: defending Deutsch's approach to probability in the Everett interpretation

- Philosophy
- 2003

Measures on the Closed Subspaces of a Hilbert Space

- Mathematics
- 1957

In his investigations of the mathematical foundations of quantum mechanics, Mackey1 has proposed the following problem: Determine all measures on the closed subspaces of a Hilbert space. A measure on…

AGAINST MANY WORLDS INTERPRETATIONS

- Philosophy
- 1990

This is a critical review of the literature on many-worlds interpretations, MWI, with arguments drawn partly from earlier critiques by Bell and Stein. The essential postulates involved in various MWI…

Unified dynamics for microscopic and macroscopic systems.

- PhysicsPhysical review. D, Particles and fields
- 1986

A modified quantum dynamics for the description of macroscopic objects is constructed and it is shown that it forbids the occurrence of linear superpositions of states localized in far-away spatial regions and induces an evolution agreeing with classical mechanics.

The Quantum Theory of Motion

- Engineering
- 1993

A lubrication and sealing system for the cylinder head of an internal combustion engine having a sleeve valve mounted for rotation therein, said sleeve valve having intake slots therethrough which…