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arXiv:quant-ph/0306180 · Physical Review Letters

Cabello Replies:

Adán Cabello

Published Jun 23, 2003• 5 citations
arXivHTMLPDF

Abstract

It is shown that Marinatto's claim [Phys. Rev. Lett. 90, 258901 (2003)] that the proof of "Bell's theorem without inequalities and without probabilities for two observers" [A. Cabello, Phys. Rev. Lett. 86, 1911 (2001)] requires four spacelike separated observers rather than two is unjustified.
DOI
10.1103/physrevlett.90.258902

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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

Comment on “Bell’s Theorem without Inequalities and without Probabilities for Two Observers”

Luca Marinatto

In this Comment we show that Cabello's argument [Phys. Rev. Lett. 86, 1911 (2001)] which proves the nonlocal feature of any classical model of quantum mechanics based on Einstein-Podolsky-Rosen (EPR) criterion of elements of reality, must involve at least four distant observers rather than the two employed by the author. Moreover we raise a remark on the necessity of performing a real experiment confirming Cabello's argument.

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A loophole in Cabello's proof to Bell's theorem without inequalities

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Cabello proved Bell's theorem without using inequalities. A loophole of Cabello's proof is pointed out in this work.

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“All versus Nothing” Inseparability for Two Observers

Adán Cabello

A recent proof of Bell's theorem without inequalities [A. Cabello, Phys. Rev. Lett. 86, 1911 (2001)] is formulated as a Greenberger-Horne-Zeilinger-type proof involving just two observers. On one hand, this new approach allows us to derive an experimentally testable Bell inequality which is violated by quantum mechanics. On the other hand, it leads to a new state-independent proof of the Kochen-Specker theorem and provides a wider perspective on the relations between the major proofs of no hidden variables.

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

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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 Probabilities for Two Observers

Adán Cabello

A proof of Bell's theorem using two maximally entangled states of two qubits is presented. It exhibits a similar logical structure to Hardy's argument of "nonlocality without inequalities." However, it works for 100% of the runs of a certain experiment. Therefore, it can also be viewed as a Greenberger-Horne-Zeilinger-like proof involving only two spacelike separated regions.

arXiv:quant-ph/0008085•Physical Review Letters•Mar 5, 2001•140 citations
A recent proof of Bell's theorem without inequalities [A. Cabello, Phys. Rev. Lett. 86, 1911 (2001)] is formulated as a Greenberger-Horne-Zeilinger-type proof involving just two observers. On one hand, this new approach allows us to derive an experimentally testable Bell inequality which is violated by quantum mechanics. On the other hand, it leads to a new state-independent proof of the Kochen-Specker theorem and provides a wider perspective on the relations between the major proofs of no hidden variables.
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).