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/0303076 · Physical Review Letters

Bell’s Theorem without Inequalities and without Alignments

Adán Cabello

Published Dec 2, 2003• 41 citations
arXivHTMLPDF

Abstract

A proof of Bell's theorem without inequalities is presented which exhibits three remarkable properties: (a). reduced local states are immune to collective decoherence; (b). distant local setups do not need to be aligned, since the required perfect correlations are achieved for any local rotation of the local setups; (c). local measurements require only individual measurements on the qubits. Indeed, it is shown that this proof is essentially the only one which fulfills (a). (b). and (c).

DOI
10.1103/physrevlett.91.230403

Related papers

Comment on “Bell's Theorem without Inequalities and without Alignments”

Luca Marinatto

In this Comment we show that Cabello's proof of Bell's theorem without inequalities [Phys. Rev. Lett. 91, 230403 (2003)] does not exhibit two of the three "remarkable properties" which the proof is claimed to possess. More precisely it is our purpose to show that property (c) of Cabello's proof, stating that ``local observables can be measured by means of tests on individual qubits" is definitely false since it has been obtained by a wrong use of the basic rules of the quantum formalism, while property (b), stating that ``distant local setups do not need to be aligned since the require perfect correlations are achieved for any local rotation of the setups", is also wrong due to the failure of validity of property (c).

arXiv:quant-ph/0409129•Physical Review Letters•Sep 17, 2004•1 citation

Bell's theorem without inequalities and without unspeakable information

Cabello, A

A proof of Bell's theorem without inequalities is presented in which distant local setups do not need to be aligned, since the required perfect correlations are achieved for any local rotation of the local setups.

•Sep 27, 2004•1 citation

Cabello Replies:

Adán Cabello

Marinatto claims that in the proof of Bell's theorem without inequalities and without alignments [A. Cabello, Phys. Rev. Lett. 91, 230403 (2003)], local observables cannot be measured by means of tests on individual qubits. Marinatto's claim is incorrect. To support this, the proof is explicitly rewritten in terms of tests on individual qubits.

arXiv:quant-ph/0409189•Physical Review Letters•Sep 17, 2004•0 citations

Bell’s theorem with and without inequalities for the three-qubit Greenberger-Horne-Zeilinger andWstates

Adán Cabello

A proof of Bell's theorem without inequalities valid for both inequivalent classes of three-qubit entangled states under local operations assisted by classical communication, namely Greenberger-Horne-Zeilinger (GHZ) and $W,$ is described. This proof leads to a Bell inequality that allows more conclusive tests of Bell's theorem for three-qubit systems. Another Bell inequality involving both tri- and bipartite correlations is introduced which illustrates the different violations of local realism exhibited by the GHZ and $W$ states.

arXiv:quant-ph/0107146•Physical Review A•Feb 5, 2002•214 citations

Rotationally invariant proof of Bell’s theorem without inequalities

Adán Cabello

The singlet state of two spin-$\frac{3}{2}$ particles allows a proof of Bell's theorem without inequalities with two distinguishing features: any local observable can be regarded as an Einstein-Podolsky-Rosen element of reality, and the contradiction with local realism occurs not only for some specific local observables but for any rotation whereof.

arXiv:quant-ph/0306073•Physical Review A•Mar 18, 2003•6 citations

Bells theorem without inequalities and only two distant observers

P. K. Aravind

A new proof of Bell’s theorem without inequalities is presented by considering an entangled state of four qubits shared between two observers. A scheme for quantum key distribution based on this proof is also discussed.

arXiv:quant-ph/0104133•Optical Fiber Communication Conference•Jan 1, 2001•41 citations
A proof of Bell's theorem without inequalities is presented which exhibits three remarkable properties: (a). reduced local states are immune to collective decoherence; (b). distant local setups do not need to be aligned, since the required perfect correlations are achieved for any local rotation of the local setups; (c). local measurements require only individual measurements on the qubits. Indeed, it is shown that this proof is essentially the only one which fulfills (a). (b). and (c).
In this Comment we show that Cabello's proof of Bell's theorem without inequalities [Phys. Rev. Lett. 91, 230403 (2003)] does not exhibit two of the three "remarkable properties" which the proof is claimed to possess. More precisely it is our purpose to show that property (c) of Cabello's proof, stating that ``local observables can be measured by means of tests on individual qubits" is definitely false since it has been obtained by a wrong use of the basic rules of the quantum formalism, while property (b), stating that ``distant local setups do not need to be aligned since the require perfect correlations are achieved for any local rotation of the setups", is also wrong due to the failure of validity of property (c).
A proof of Bell's theorem without inequalities valid for both inequivalent classes of three-qubit entangled states under local operations assisted by classical communication, namely Greenberger-Horne-Zeilinger (GHZ) and W,W,W, is described. This proof leads to a Bell inequality that allows more conclusive tests of Bell's theorem for three-qubit systems. Another Bell inequality involving both tri- and bipartite correlations is introduced which illustrates the different violations of local realism exhibited by the GHZ and WWW states.
The singlet state of two spin-32\frac{3}{2}23​ particles allows a proof of Bell's theorem without inequalities with two distinguishing features: any local observable can be regarded as an Einstein-Podolsky-Rosen element of reality, and the contradiction with local realism occurs not only for some specific local observables but for any rotation whereof.