Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Philosophy of Science

Another No-go Theorem for Hidden Variable Models of Inaccurate Spin 1 Measurements

Thomas Breuer

Published Dec 1, 2003• 4 citations
Publisher

Abstract

Uncertainty about the actual orientation of the measurement device has been claimed to open a loophole for hidden variable models of quantum mechanics. In this paper I describe the statistics of inaccurate spin measurements by unsharp spin observables. A no-go theorem for hidden variable models of the inaccurate measurement statistics follows: There is a finite set of directions for which not all results of inaccurate spin measurements can be predetermined in a non-contextual way. In contrast to an earlier theorem (Breuer 2002) this result does not rely on the assigment of approximate truth values, and it holds under weaker assumptions on the measurement inaccuracy.

DOI
10.1086/377414

Related papers

Kochen-Specker Theorem for Finite Precision Spin-One Measurements

Thomas Breuer

Unsharp spin-one observables arise from the fact that a residual uncertainty about the actual orientation of the measurement device remains. If the uncertainty is below a certain level, and if the distribution of measurement errors is covariant under rotations, a Kochen-Specker theorem for the unsharp spin observables follows: There are finite sets of directions such that not all the unsharp spin observables in these directions can consistently be assigned approximate truth values in a noncontextual way.

arXiv:quant-ph/0206035•Physical Review Letters•May 29, 2002•15 citations

Simulating quantum mechanics by non-contextual hidden variables

Rob Clifton, Adrian Kent

No physical measurement can be performed with infinite precision. This leaves a loophole in the standard no–go arguments against non–contextual hidden variables. All such arguments rely on choosing special sets of quantum–mechanical observables with measurement outcomes that cannot be simulated non–contextually. As a consequence, these arguments do not exclude the hypothesis that the class of physical measurements in fact corresponds to a dense subset of all theoretically possible measurements with outcomes and quantum probabilities that can be recovered from a non–contextual hidden–variable model. We show here by explicit construction that there are indeed such non–contextual hidden–variable models, both for projection–valued and positive–operator–valued measurements.

arXiv:quant-ph/9908031•Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences•Sep 8, 2000•93 citations

some results on unsharp localization in quantum mechanics

CATTANEO G., Tiziana Marsico, Giuseppe Antonio NISTICO'

Some no go theorems in standard quantum mechanics on Hibert spaces, on the non-localizability of zero mass, non-zero spin particles by sharp observables, i.e., projection valued (PV) measures, are introduced. The solution by unsharp observables, i.e., POV measures is presented and the relationship with the induced inner and outer PV measures (or PV rough approximations) is discussed.

•Jan 1, 1998•0 citations

Unsharp eigenvalues and quantum contextuality

F. De Zela

The Kochen-Specker theorem, Bell inequalities, and several other tests that were designed to rule out hidden-variable theories, assume the existence of observables having infinitely sharp eigenvalues. A paradigmatic example is spin-1/2. It is measured with a Stern-Gerlach array whose outputs are divided into two classes, spin-up and spin-down, in correspondence to the two spots observed on a detection screen. The spot's finite size is attributed to imperfections of the measuring device. This assumption turns the experimental output into a dichotomic, discrete one, thereby allowing the assignment of each spot to an infinitely sharp eigenvalue. Alternatively, one can assume that the spot's finite size stems from eigenvalues spanning a continuous range. Can we disprove such an assumption? Can we rule out hidden-variable theories that reproduce quantum predictions by assuming that, e.g., the electron's magnetic moment is not exactly the same for all electrons? We address these questions by focusing on the Peres-Mermin version of the Bell-Kochen-Specker theorem. It is shown that the assumption of unsharp eigenvalues precludes ruling out non-contextual hidden-variable theories and hence quantum contextuality does not arise. Analogous results hold for Bell-like inequalities. This represents a new loophole that spoils several fundamental tests of quantum mechanics and issues the challenge to close it.

arXiv:1410.0409•Oct 1, 2014•0 citations

An investigation of no-go theorems in hidden variable models of quantum mechanics

Navid Siami

Realism defined in EPR paper as “In a complete theory there is an element corresponding to each element of reality.” Bell showed that there is a forbidden triangle (Realism, Quantum Statistics, and Locality), and we are only allowed to pick two out of three. In this thesis, we investigate other inequalities and no-go theorems that we face. We also discuss possible Hidden Variable Models that are tailored to be consistent with Quantum Mechanics and the specific no-go theorems. In the special case of the Leggett Inequality the proposed hidden variable is novel in the sense that the hidden variable is in the measurement device rather than the wave-function.

•Jan 1, 2016•1 citation

Hidden-Variable Theories

Reinhold A. Bertlmann, Nicolai Friis

Abstract In chapter 12 we give an overview of the historical development of hidden-variable theories aiming to attribute ‘hidden’ definite outcomes to any potential measurement on a quantum system. We start with a discussion of von Neumann’s assumption on hidden-variable models, which was later realized not to hold by Hermann, Kochen, Specker, and Bell, going into detail on Bell’s refutation of von Neumann’s arguments. We then turn to the notion of contextuality, which severely restricts hidden-variable models: we discuss Gleason’s theorem before stating and proving the famous Kochen-Specker theorem, as well as the simpler versions of Peres’ nonet and Mermin’s pentagram. These results show that quantum mechanics is not compatible with the assignment of definite measurement outcomes to all possible measurements, and such assignments can hence only be made once a restricted set of observables, a context, is selected

•Sep 7, 2023•0 citations
Uncertainty about the actual orientation of the measurement device has been claimed to open a loophole for hidden variable models of quantum mechanics. In this paper I describe the statistics of inaccurate spin measurements by unsharp spin observables. A no-go theorem for hidden variable models of the inaccurate measurement statistics follows: There is a finite set of directions for which not all results of inaccurate spin measurements can be predetermined in a non-contextual way. In contrast to an earlier theorem (Breuer 2002) this result does not rely on the assigment of approximate truth values, and it holds under weaker assumptions on the measurement inaccuracy.
Unsharp spin-one observables arise from the fact that a residual uncertainty about the actual orientation of the measurement device remains. If the uncertainty is below a certain level, and if the distribution of measurement errors is covariant under rotations, a Kochen-Specker theorem for the unsharp spin observables follows: There are finite sets of directions such that not all the unsharp spin observables in these directions can consistently be assigned approximate truth values in a noncontextual way.
No physical measurement can be performed with infinite precision. This leaves a loophole in the standard no–go arguments against non–contextual hidden variables. All such arguments rely on choosing special sets of quantum–mechanical observables with measurement outcomes that cannot be simulated non–contextually. As a consequence, these arguments do not exclude the hypothesis that the class of physical measurements in fact corresponds to a dense subset of all theoretically possible measurements with outcomes and quantum probabilities that can be recovered from a non–contextual hidden–variable model. We show here by explicit construction that there are indeed such non–contextual hidden–variable models, both for projection–valued and positive–operator–valued measurements.
The Kochen-Specker theorem, Bell inequalities, and several other tests that were designed to rule out hidden-variable theories, assume the existence of observables having infinitely sharp eigenvalues. A paradigmatic example is spin-1/2. It is measured with a Stern-Gerlach array whose outputs are divided into two classes, spin-up and spin-down, in correspondence to the two spots observed on a detection screen. The spot's finite size is attributed to imperfections of the measuring device. This assumption turns the experimental output into a dichotomic, discrete one, thereby allowing the assignment of each spot to an infinitely sharp eigenvalue. Alternatively, one can assume that the spot's finite size stems from eigenvalues spanning a continuous range. Can we disprove such an assumption? Can we rule out hidden-variable theories that reproduce quantum predictions by assuming that, e.g., the electron's magnetic moment is not exactly the same for all electrons? We address these questions by focusing on the Peres-Mermin version of the Bell-Kochen-Specker theorem. It is shown that the assumption of unsharp eigenvalues precludes ruling out non-contextual hidden-variable theories and hence quantum contextuality does not arise. Analogous results hold for Bell-like inequalities. This represents a new loophole that spoils several fundamental tests of quantum mechanics and issues the challenge to close it.
Realism defined in EPR paper as “In a complete theory there is an element corresponding to each element of reality.” Bell showed that there is a forbidden triangle (Realism, Quantum Statistics, and Locality), and we are only allowed to pick two out of three. In this thesis, we investigate other inequalities and no-go theorems that we face. We also discuss possible Hidden Variable Models that are tailored to be consistent with Quantum Mechanics and the specific no-go theorems. In the special case of the Leggett Inequality the proposed hidden variable is novel in the sense that the hidden variable is in the measurement device rather than the wave-function.
Abstract In chapter 12 we give an overview of the historical development of hidden-variable theories aiming to attribute ‘hidden’ definite outcomes to any potential measurement on a quantum system. We start with a discussion of von Neumann’s assumption on hidden-variable models, which was later realized not to hold by Hermann, Kochen, Specker, and Bell, going into detail on Bell’s refutation of von Neumann’s arguments. We then turn to the notion of contextuality, which severely restricts hidden-variable models: we discuss Gleason’s theorem before stating and proving the famous Kochen-Specker theorem, as well as the simpler versions of Peres’ nonet and Mermin’s pentagram. These results show that quantum mechanics is not compatible with the assignment of definite measurement outcomes to all possible measurements, and such assignments can hence only be made once a restricted set of observables, a context, is selected