# On Zurek’s Derivation of the Born Rule

@article{Schlosshauer2005OnZD, title={On Zurek’s Derivation of the Born Rule}, author={Maximilian Schlosshauer and Arthur I. Fine}, journal={Foundations of Physics}, year={2005}, volume={35}, pages={197-213} }

Recently, W. H. Zurek presented a novel derivation of the Born rule based on a mechanism termed environment-assisted invariance, or “envariance” [W. H. Zurek, Phys. Rev. Lett. 90(2), 120404 (2003)]. We review this approach and identify fundamental assumptions that have implicitly entered into it, emphasizing issues that any such derivation is likely to face.

## 68 Citations

Derivations of the Born Rule

- MathematicsJerusalem 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

- 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…

Quantum probabilities from combination of Zurekʼs envariance and Gleasonʼs theorem

- Mathematics, Physics
- 2014

The quantum-mechanical rule for probabilities, in its most general form of positive-operator valued measure, is shown to be a consequence of the environment-assisted invariance (envariance) idea…

Zurek’s envariance derivation of Born’s rule and measurement

- Mathematics, Physics
- 2012

Zurek’s derivation of Born’s rule using envariance (invariance due to entanglement) is considered to capture the probability in full generality, but only as applied to the measurement of a quantum…

Born Rule and Noncontextual Probability

- Mathematics, Physics
- 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…

Born Rule and its Interpretation

- History, Computer ScienceCompendium 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…

On the Explanation of Born-Rule Statistics in the de Broglie-Bohm Pilot-Wave Theory

- Mathematics, MedicineEntropy
- 2018

It is suggested that there is somewhat less conflict between the two approaches than existing polemics might suggest, and that indeed elements from both arguments may be combined to provide a unified and fully-compelling explanation from the postulated dynamical first principles, of the Born rule.

Quantum probability law from ‘environment-assisted invariance’ in terms of pure-state twin unitaries

- Physics, Mathematics
- 2007

Zurek's derivation of the Born rule from envariance (environment-assisted invariance) is retraced in an attempt to present a more detailed derivation, which is extended to encompass the trace-rule…

Many-particle interference to test Born's rule

- Physics
- 2020

Born's rule, one of the cornerstones of quantum mechanics, relates detection probabilities to the modulus square of the wave function. Single-particle interference is accordingly limited to pairs of…

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

- Physics
- 2017

A new approach to wavefunction collapse is prepared by an analysis of semiclassical gravity. The fact that, in semiclassical gravity, superposed states must share a common classical spacetime…

## References

SHOWING 1-10 OF 29 REFERENCES

Derivation of the Born rule from operational assumptions

- Computer Science, PhysicsProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- 2004

The Born rule is derived from operational assumptions, together with assumptions of quantum mechanics that concern only the deterministic development of the state, and provides a probability rule for state spaces that are not Hilbert spaces.

PROBABILITIES FROM ENVARIANCE

- Physics
- 2004

Zurek claims to have derived Born's rule noncircularly in the context of an ontological no-collapse interpretation of quantum states, without any "deus ex machina imposition of the symptoms of…

No-signalling-based version of Zurek's derivation of quantum probabilities: A note on "Environment-assisted invariance, entanglement, and probabilities in quantum physics"

- Physics, Mathematics
- 2003

Zurek has derived the quantum probabilities for Schmidt basis states of bipartite quantum systems in pure joint states, from the assumption that they should be not be affected by one party's action…

The Everett Interpretation

- Philosophy
- 1984

We begin with an essentially technical notion that will be used repeatedly in what follows. Indeed, it will serve as our conduit between physical observations and the mathematical formalism of…

The Everett Interpretation of Quantum Mechanics: Many Worlds or None?

- Philosophy
- 1984

The doctoral dissertation of Hugh Everett, III-written under the direction of J. A. Wheeler-was principally motivated by the wish to obtain a reasonable basis for the quantization of general…

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

- Philosophy, Physics
- 2003

An analysis is made of Deutsch's recent claim to have derived the Born rule from decision-theoretic assumptions. It is argued that Deutsch's proof must be understood in the explicit context of the…

How probability arises in quantum mechanics

- Physics
- 1989

Abstract A version of the postulates of quantum mechanics is presented in which no reference is made to probability. Instead we rely on a weaker postulate referring to eigenvalues and eigenstates.…

Decoherence, einselection, and the quantum origins of the classical

- Physics
- 2003

as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus…

Decoherence, the measurement problem, and interpretations of quantum mechanics

- Physics
- 2005

Environment-induced decoherence and superselection have been a subject of intensive research over the past two decades, yet their implications for the foundational problems of quantum mechanics, most…

AGAINST MANY WORLDS INTERPRETATIONS

- Physics
- 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…