# All quantum observables in a hidden-variable model must commute simultaneously

@article{Malley2004AllQO, title={All quantum observables in a hidden-variable model must commute simultaneously}, author={James D. Malley}, journal={Physical Review A}, year={2004}, volume={69}, pages={022118} }

Under a standard set of assumptions for a hidden-variable model for quantum events we show that all observables must commute simultaneously. This seems to be an ultimate statement about the inapplicability of the usual hidden-variable model for quantum events. And, despite Bell's complaint that a key condition of von Neumann's was quite unrealistic, we show that these conditions, under which von Neumann produced the first no-go proof, are entirely equivalent to those introduced by Bell and…

## 39 Citations

Comment on “All quantum observables in a hidden-variable model must commute simultaneously”

- Physics
- 2006

Malley discussed [Phys. Rev. A 69, 022118 (2004)] that all quantum observables in a hidden-variable model for quantum events must commute simultaneously. In this comment, we discuss that Malley's…

Classical Probability and Quantum Outcomes

- MathematicsAxioms
- 2014

An essential task here is a closer identification of this conflict based on deriving commutativity from the weakest possible assumptions, and showing that stronger assumptions in some of the existing no-go proofs are unnecessary.

Local realism does not impose the commutative algebraic structure into all quantum observables

- Physics, Philosophy
- 2013

Malley and Fine (Phys. Rev. A 2006 73 066102) discussed that all quantum observables would commute simultaneously if we accept a realistic theory of the Bell type (a local realistic theory) for…

Logical Difficulty from Combining Counterfactuals in the GHZ-Bell Theorems

- Physics
- 2013

In eliminating the fair sampling assumption, the
Greenberger, Horne, Zeilinger (GHZ) theorem is believed to confirm Bell’s
historic conclusion that local hidden variables are inconsistent with the…

A principle of quantumness

- Physics
- 2014

Quantum correlations and other phenomena characteristic to a quantum world can be understood as simply consequences of a principle derived from the postulates of Quantum Mechanics. This explanatory…

Quantum-collapse Bell inequalities

- Physics
- 2014

Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2, CanadaWe propose Bell inequalities for discrete or continuous quantum systems which test the compati-bility of…

Quasi-Bell inequalities from symmetrized products of noncommuting qubit observables

- Physics
- 2015

Noncommuting observables cannot be simultaneously measured, however, under local hidden variable models, they must simultaneously hold premeasurement values, implying the existence of a joint…

Excluding joint probabilities from quantum theory

- Mathematics
- 2018

Quantum theory does not provide a unique definition for the joint probability of two non-commuting observables, which is the next important question after the Born's probability for a single…

Quantum Cryptographic Security from Contextuality Gelo

- Computer Science, Mathematics
- 2011

Device-independent security from contextuality is demonstrated by considering a distributed box of Peres-Mermin observables for the Kochen Specker theorem and the security of the corresponding key distribution protocol is certified by checking for not-too-strong violations of Bell inequalities.

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