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

arXiv:quant-ph/0309172 · Physical Review Letters

Proposed Experiment to Test the Bounds of Quantum Correlations

Adán Cabello

Published Feb 12, 2004• 17 citations
arXivHTMLPDF

Abstract

The combination of quantum correlations appearing in the Clauser-Horne-Shimony-Holt inequality can give values between the classical bound, 2, and Tsirelson's bound, 2 x square root of 2. However, for a given set of local observables, there are values in this range which no quantum state can attain. We provide the analytical expression for the corresponding bound for a parametrization of the local observables introduced by Filipp and Svozil, and describe how to experimentally trace it using a source of singlet states. Such an experiment will be useful to identify the origin of the experimental errors in Bell's inequality-type experiments and could be modified to detect hypothetical correlations beyond those predicted by quantum mechanics.

DOI
10.1103/physrevlett.92.060403

Related papers

Experimental Evidence for Bounds on Quantum Correlations

Fabio Antonio Bovino, Giuseppe Castagnoli, Ivo Pietro Degiovanni +1 more

We implemented the experiment proposed by Cabello in the preceding Letter to test the bounds of quantum correlation. As expected from the theory we found that, for certain choices of local observables, Tsirelson's bound of the Clauser-Horne-Shimony-Holt inequality (2 x square root of 2) is not reached by any quantum states.

arXiv:quant-ph/0310042•Physical Review Letters•Feb 12, 2004•13 citations

Approaching Tsirelson’s Bound in a Photon Pair Experiment

Hou Shun Poh, Siddarth Koduru Joshi, Alessandro Ceré +2 more

We present an experimental test of the Clauser-Horne-Shimony-Holt Bell inequality on photon pairs in a maximally entangled state of polarization in which a value S=2.82759±0.00051 is observed. This value comes close to the Tsirelson bound of |S|≤2sqrt[2], with S-2sqrt[2]=0.00084±0.00051. It also violates the bound |S|≤2.82537 introduced by Grinbaum by 4.3 standard deviations. This violation allows us to exclude that quantum mechanics is only an effective description of a more fundamental theory.

arXiv:1506.01865•Physical Review Letters•Oct 30, 2015•57 citations

Experimental Violation of Bell’s Inequality beyond Tsirelson’s Bound

Yu-Ao Chen, Tao Yang, An‐Ning Zhang +3 more

The correlations between two qubits belonging to a three-qubit system can violate the Clauser-Horne-Shimony-Holt-Bell inequality beyond Tsirelson's bound [A. Cabello, Phys. Rev. Lett. 88, 060403 (2002)]. We experimentally demonstrate such a violation by 7 standard deviations by using a three-photon polarization-entangled Greenberger-Horne-Zeilinger state produced by Type-II spontaneous parametric down-conversion. In addition, using part of our results, we obtain a violation of the Mermin inequality by 39 standard deviations.

arXiv:quant-ph/0607194•Physical Review Letters•Oct 27, 2006•21 citations

Clauser-Horne-Shimony-Holt correlation and Clauser-Horne correlation do not lead to the largest violations of Bell’s inequality

M. Ardehali

An inequality is deduced from Einstein's locality and a supplementary assumption. This inequality defines an experiment that can actually be performed with present technology to test local realism. Quantum mechanics violates this inequality a factor of 1.5. In contrast, quantum mechanics violates previous inequalities [for example, those of J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969); S. J. Freedman and I. F. Clauser ibid. 28, 938 (1972); and J. F. Clauser and M. A. Horne, Phys. Rev. D 10, 526 (1974)] by a factor of $\sqrt{2}.$ Thus the magnitude of violation of the inequality derived in this paper is approximately 20.7% larger than the magnitude of violation of previous inequalities. This result can be particularly important for the experimental test of locality.

arXiv:quant-ph/9701032•Physical Review A•Jan 1, 1998•5 citations

Tsirelson bounds for generalized Clauser-Horne-Shimony-Holt inequalities

Stephanie Wehner

Quantum theory imposes a strict limit on the strength of nonlocal correlations. It only allows for a violation of the Clauser, Horne, Shimony, and Holt (CHSH) inequality up to the value $2\sqrt{2}$, known as Tsirelson's bound. In this paper, we consider generalized CHSH inequalities based on many measurement settings with two possible measurement outcomes each. We demonstrate how to prove Tsirelson bounds for any such generalized CHSH inequality using semidefinite programming. As an example, we show that for any shared entangled state and observables ${X}_{1},\dots{},{X}_{n}$ and ${Y}_{1},\dots{},{Y}_{n}$ with eigenvalues $\ifmmode\pm\else\textpm\fi{}1$ we have $\ensuremath{\mid}⟨{X}_{1}{Y}_{1}⟩+⟨{X}_{2}{Y}_{1}⟩+⟨{X}_{2}{Y}_{2}⟩+⟨{X}_{3}{Y}_{2}⟩+\ensuremath{\cdots}+⟨{X}_{n}{Y}_{n}⟩\ensuremath{-}⟨{X}_{1}{Y}_{n}⟩\ensuremath{\mid}\ensuremath{\leqslant}2n\phantom{\rule{0.2em}{0ex}}\mathrm{cos}[\ensuremath{\pi}∕(2n)]$. It is well known that there exist observables such that equality can be achieved. However, we show that these are indeed optimal. Our approach can easily be generalized to other inequalities for such observables.

arXiv:quant-ph/0510076•Physical Review A•Feb 14, 2006•170 citations

A Bell inequality which can be used to test locality more simply than Clauser-Horne inequality and which is violated by a larger magnitude of violation than Clauser-Horne-Shimony-Holt inequality

M. Ardehali

A correlation inequality is derived from local realism and a supplementary assumption. Unlike Clauser-Horne (CH) inequality [or Clauser-Horne-Shimony-Holt (CHSH) inequality] which is violated by quantum mechanics by a factor of $\sqrt 2$, this inequality is violated by a factor of 1.5. Thus the magnitude of violation of this inequality is approximately 20.7% larger than the magnitude of violation of previous inequalities. Moreover, unlike CH (or CHSH) inequality which requires the measurement of five detection probabilities, the present inequality requires the measurement of only two detection probabilities. This inequality can therefore be used to test locality more simply than CH or CHSH inequality.

arXiv:quant-ph/9709043•Sep 19, 1997•0 citations
The combination of quantum correlations appearing in the Clauser-Horne-Shimony-Holt inequality can give values between the classical bound, 2, and Tsirelson's bound, 2 x square root of 2. However, for a given set of local observables, there are values in this range which no quantum state can attain. We provide the analytical expression for the corresponding bound for a parametrization of the local observables introduced by Filipp and Svozil, and describe how to experimentally trace it using a source of singlet states. Such an experiment will be useful to identify the origin of the experimental errors in Bell's inequality-type experiments and could be modified to detect hypothetical correlations beyond those predicted by quantum mechanics.
We present an experimental test of the Clauser-Horne-Shimony-Holt Bell inequality on photon pairs in a maximally entangled state of polarization in which a value S=2.82759±0.00051 is observed. This value comes close to the Tsirelson bound of |S|≤2sqrt[2], with S-2sqrt[2]=0.00084±0.00051. It also violates the bound |S|≤2.82537 introduced by Grinbaum by 4.3 standard deviations. This violation allows us to exclude that quantum mechanics is only an effective description of a more fundamental theory.
The correlations between two qubits belonging to a three-qubit system can violate the Clauser-Horne-Shimony-Holt-Bell inequality beyond Tsirelson's bound [A. Cabello, Phys. Rev. Lett. 88, 060403 (2002)]. We experimentally demonstrate such a violation by 7 standard deviations by using a three-photon polarization-entangled Greenberger-Horne-Zeilinger state produced by Type-II spontaneous parametric down-conversion. In addition, using part of our results, we obtain a violation of the Mermin inequality by 39 standard deviations.
An inequality is deduced from Einstein's locality and a supplementary assumption. This inequality defines an experiment that can actually be performed with present technology to test local realism. Quantum mechanics violates this inequality a factor of 1.5. In contrast, quantum mechanics violates previous inequalities [for example, those of J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969); S. J. Freedman and I. F. Clauser ibid. 28, 938 (1972); and J. F. Clauser and M. A. Horne, Phys. Rev. D 10, 526 (1974)] by a factor of 2.\sqrt{2}.2​. Thus the magnitude of violation of the inequality derived in this paper is approximately 20.7% larger than the magnitude of violation of previous inequalities. This result can be particularly important for the experimental test of locality.
Quantum theory imposes a strict limit on the strength of nonlocal correlations. It only allows for a violation of the Clauser, Horne, Shimony, and Holt (CHSH) inequality up to the value 222\sqrt{2}22​, known as Tsirelson's bound. In this paper, we consider generalized CHSH inequalities based on many measurement settings with two possible measurement outcomes each. We demonstrate how to prove Tsirelson bounds for any such generalized CHSH inequality using semidefinite programming. As an example, we show that for any shared entangled state and observables X1,…,Xn{X}_{1},\dots{},{X}_{n}X1​,…,Xn​ and Y1,…,Yn{Y}_{1},\dots{},{Y}_{n}Y1​,…,Yn​ with eigenvalues $\ifmmode\pm\else\textpm\fi{}1$ we have $\ensuremath{\mid}⟨{X}_{1}{Y}_{1}⟩+⟨{X}_{2}{Y}_{1}⟩+⟨{X}_{2}{Y}_{2}⟩+⟨{X}_{3}{Y}_{2}⟩+\ensuremath{\cdots}+⟨{X}_{n}{Y}_{n}⟩\ensuremath{-}⟨{X}_{1}{Y}_{n}⟩\ensuremath{\mid}\ensuremath{\leqslant}2n\phantom{\rule{0.2em}{0ex}}\mathrm{cos}[\ensuremath{\pi}∕(2n)]$. It is well known that there exist observables such that equality can be achieved. However, we show that these are indeed optimal. Our approach can easily be generalized to other inequalities for such observables.
A correlation inequality is derived from local realism and a supplementary assumption. Unlike Clauser-Horne (CH) inequality [or Clauser-Horne-Shimony-Holt (CHSH) inequality] which is violated by quantum mechanics by a factor of 2\sqrt 22​, this inequality is violated by a factor of 1.5. Thus the magnitude of violation of this inequality is approximately 20.7% larger than the magnitude of violation of previous inequalities. Moreover, unlike CH (or CHSH) inequality which requires the measurement of five detection probabilities, the present inequality requires the measurement of only two detection probabilities. This inequality can therefore be used to test locality more simply than CH or CHSH inequality.