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

IEEE International Symposium on Information Theory (ISIT)

Quantum pseudo-telepathy and the kochen-specker theorem

Renato Renner, Stefan Wolf

Published Dec 23, 2004• 23 citations
Publisher

Abstract

There are different approaches to proving the impossibility of classical hidden-variable explanations of quantum-mechanical behavior. Whereas Kochen and Specker proved that a three-or higher-dimensional quantum-mechanical system cannot be "classically" prepared for all possible alternative measurements in a consistent way, Bell showed that the behavior of certain two-partite systems is nonlocal, i.e., inexplicable by shared classical information. We show a close connection between deterministic manifestations of such nonlocality-called "pseudotelepathy" games-and Kochen and Specker's theorem: Every such game leads to a Kochen-Specker contradiction, and vice versa

DOI
10.1109/isit.2004.1365359

Related papers

Kochen-Specker Theorem and Games

Laura Mančinska

One of the statements one would hear pretty early in any quantum mechanics course is that for quantum particles there are properties which do not have definite values. For example, if we measure |+〉 in standard basis, the best we can do to describe the outcome is to say, that with probability 1/2 we will get 0 and with probability 1/2 we will get 1. Yet one could wonder, is this really the way things are or is it just because our description of this quantum particle is incomplete, but in fact there are some hidden variables inside every quantum system that contain enough information to tell the outcome of measurement (see Fig. 1). However, many people disdain the idea of hidden variables, so there has been rather long history of theorems that forbid theories involving hidden variables. Usually if one wants to prove some no hidden variables theorem he has to assume something about the hidden variables theories he is going to forbid. One of such assumptions is non-contextuality, which means that the outcome we get after measuring with an observable is the same regardless of what other observables we choose to measure at the same time. The first theorem forbidding hidden variables theories is due to von Neumann in 1932. Then for a third of a century everyone cited von Neumann’s work carelessly, till Bell in 1966 indicated that there was an unreasonable assumption in von Neumann’s proof and urged for further examination of the problem (see [6] and [1] for more historical details). Bell also constructed a hidden variables model for one qubit that could assign the outcome of any observable in a way consistent with quantum mechanics. He also proved two theorems that forbid non-contextual hidden variables theories using counterexamples with larger quantum systems. Yet surprisingly he himself thought that hidden variables do exists and considered these theorems only as characterizations of the hidden variables theory we should look for. In this essay we will discuss several versions of one of the two Bell’s theorems. The theorem we will consider was also independently proven by Kochen and Specker in 1967 (see [5]), hence it is called Bell-Kochen-Specker theorem. For shortness and in order not to mix this theorem with another Bell’s theorem from now on we will refer to it as Kochen-Specker theorem. We will be interested in proving several versions of this theorem and the following lemma will turn out to be of great use:

•Jan 1, 2007•0 citations

Hidden Variables and Nonlocality in Quantum Mechanics

Douglas L. Hemmick

In this paper, we show that Erwin Schroedinger's generalization of the Einstein Podolsky Rosen argument can be connected to certain mathematical theorems - Gleason's and also Kochen and Specker's - in a manner analogous to the relation of EPR itself with Bell's theorem. In both cases, the conclusion is quantum nonlocality, as we discuss. The "Schroedinger nonlocality" proofs share some features with the Greenberger, Horne, and Zeilinger quantum-nonlocality work, yet also differ in significant ways. For clarity and completeness, we begin with a detailed discussion of the topic of hidden variable theorems. We argue, in agreement with John S. Bell, that 'impossibility' does not follow.

arXiv:quant-ph/0412011•Dec 2, 2004•13 citations

Two theorems of Jhon Bell and Communication Complexity

Guruprasad Kar

John Bell taught us that quantum mechanics can not be reproduced by non-contextual and local Hidden variable theory. The impossibility of replacing quantum mechanics by non-contextual Hidden Variable Theory can be turned to a impossible coloring pseudo-telepathy game to be played by two distant players. The game can not be won without communication in the classical world. But if the players share entangled state (quantum correlation) the game can be won deterministically using no communication. This again shows that though quantum correlation can not be used for communication, two parties can not simulate quantum correlation without classical communication. The motivation of the article is to present the earlier works on Hidden Variable Theory and recently developed pseudo-telepathy problem in a simpler way, which may be helpful for the beginners in this area.

arXiv:quant-ph/0504191•Apr 26, 2005•0 citations

Understanding quantum non-locality through pseudo-telepathy game

Samir Kunkri

Usually by quantum non‐locality we mean that quantum mechanics can not be replaced by local realistic theory. On the other hand this nonlocal feature of quantum mechanics can not be used for instantaneous communication and hence it respect Einstein’s special theory of relativity. But still it is not trivial as proved by various quantum information processing using entangled states. Recently there have been studies of hypothetical non‐local system again respecting no‐signalling which is beyond quantum mechanics. Here we study the power of such a hypothetical nonlocal box first suggested by Popescu et.al. in the context of recently suggested pseudo‐telepathy game constructed from a Kochen‐Specker set.

AIP conference proceedings•Jan 1, 2006•0 citations

Experimental Implementation of a Kochen-Specker Set of Quantum Tests

Vincenzo D’Ambrosio, Isabelle Herbauts, Elias Amselem +4 more

The Kochen-Specker theorem, which excludes noncontextual hidden-variable explanations for the counterintuitive puzzles of quantum mechanics, has been realized for the first time in two different single-photon experiments.

arXiv:1209.1836•Physical Review X•Feb 14, 2013•83 citations

Noncontextual Hidden Variables and Physical Measurements

Adrian Kent

Meyer [Phys. Rev. Lett. 83, 3751 (1999)] recently showed that the Kochen-Specker theorem, which demonstrates the impossibility of a deterministic hidden variable description of ideal spin measurements on a spin 1 particle, can be effectively nullified if only finite precision measurements are considered. We generalize this result: one can ascribe consistent outcomes to a dense subset of the set of projection valued measurements, or to a dense subset of the set of positive operator valued measurements, on any finite dimensional system. Hence no Kochen-Specker-like contradiction can rule out hidden variable theories indistinguishable from quantum theory by finite precision measurements in either class.

arXiv:quant-ph/9906006•Physical Review Letters•Nov 8, 1999•103 citations
There are different approaches to proving the impossibility of classical hidden-variable explanations of quantum-mechanical behavior. Whereas Kochen and Specker proved that a three-or higher-dimensional quantum-mechanical system cannot be "classically" prepared for all possible alternative measurements in a consistent way, Bell showed that the behavior of certain two-partite systems is nonlocal, i.e., inexplicable by shared classical information. We show a close connection between deterministic manifestations of such nonlocality-called "pseudotelepathy" games-and Kochen and Specker's theorem: Every such game leads to a Kochen-Specker contradiction, and vice versa
One of the statements one would hear pretty early in any quantum mechanics course is that for quantum particles there are properties which do not have definite values. For example, if we measure |+〉 in standard basis, the best we can do to describe the outcome is to say, that with probability 1/2 we will get 0 and with probability 1/2 we will get 1. Yet one could wonder, is this really the way things are or is it just because our description of this quantum particle is incomplete, but in fact there are some hidden variables inside every quantum system that contain enough information to tell the outcome of measurement (see Fig. 1). However, many people disdain the idea of hidden variables, so there has been rather long history of theorems that forbid theories involving hidden variables. Usually if one wants to prove some no hidden variables theorem he has to assume something about the hidden variables theories he is going to forbid. One of such assumptions is non-contextuality, which means that the outcome we get after measuring with an observable is the same regardless of what other observables we choose to measure at the same time. The first theorem forbidding hidden variables theories is due to von Neumann in 1932. Then for a third of a century everyone cited von Neumann’s work carelessly, till Bell in 1966 indicated that there was an unreasonable assumption in von Neumann’s proof and urged for further examination of the problem (see [6] and [1] for more historical details). Bell also constructed a hidden variables model for one qubit that could assign the outcome of any observable in a way consistent with quantum mechanics. He also proved two theorems that forbid non-contextual hidden variables theories using counterexamples with larger quantum systems. Yet surprisingly he himself thought that hidden variables do exists and considered these theorems only as characterizations of the hidden variables theory we should look for. In this essay we will discuss several versions of one of the two Bell’s theorems. The theorem we will consider was also independently proven by Kochen and Specker in 1967 (see [5]), hence it is called Bell-Kochen-Specker theorem. For shortness and in order not to mix this theorem with another Bell’s theorem from now on we will refer to it as Kochen-Specker theorem. We will be interested in proving several versions of this theorem and the following lemma will turn out to be of great use:
In this paper, we show that Erwin Schroedinger's generalization of the Einstein Podolsky Rosen argument can be connected to certain mathematical theorems - Gleason's and also Kochen and Specker's - in a manner analogous to the relation of EPR itself with Bell's theorem. In both cases, the conclusion is quantum nonlocality, as we discuss. The "Schroedinger nonlocality" proofs share some features with the Greenberger, Horne, and Zeilinger quantum-nonlocality work, yet also differ in significant ways. For clarity and completeness, we begin with a detailed discussion of the topic of hidden variable theorems. We argue, in agreement with John S. Bell, that 'impossibility' does not follow.
John Bell taught us that quantum mechanics can not be reproduced by non-contextual and local Hidden variable theory. The impossibility of replacing quantum mechanics by non-contextual Hidden Variable Theory can be turned to a impossible coloring pseudo-telepathy game to be played by two distant players. The game can not be won without communication in the classical world. But if the players share entangled state (quantum correlation) the game can be won deterministically using no communication. This again shows that though quantum correlation can not be used for communication, two parties can not simulate quantum correlation without classical communication. The motivation of the article is to present the earlier works on Hidden Variable Theory and recently developed pseudo-telepathy problem in a simpler way, which may be helpful for the beginners in this area.
Usually by quantum non‐locality we mean that quantum mechanics can not be replaced by local realistic theory. On the other hand this nonlocal feature of quantum mechanics can not be used for instantaneous communication and hence it respect Einstein’s special theory of relativity. But still it is not trivial as proved by various quantum information processing using entangled states. Recently there have been studies of hypothetical non‐local system again respecting no‐signalling which is beyond quantum mechanics. Here we study the power of such a hypothetical nonlocal box first suggested by Popescu et.al. in the context of recently suggested pseudo‐telepathy game constructed from a Kochen‐Specker set.
Meyer [Phys. Rev. Lett. 83, 3751 (1999)] recently showed that the Kochen-Specker theorem, which demonstrates the impossibility of a deterministic hidden variable description of ideal spin measurements on a spin 1 particle, can be effectively nullified if only finite precision measurements are considered. We generalize this result: one can ascribe consistent outcomes to a dense subset of the set of projection valued measurements, or to a dense subset of the set of positive operator valued measurements, on any finite dimensional system. Hence no Kochen-Specker-like contradiction can rule out hidden variable theories indistinguishable from quantum theory by finite precision measurements in either class.