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/9712055 · Physical Review A

Ladder proof of nonlocality without inequalities and without probabilities

Adán Cabello

Published Sep 1, 1998• 18 citations
arXivHTMLPDF

Abstract

The ladder proof of nonlocality without inequalities for two spin-$\frac{1}{2}$ particles proposed by Hardy [in New Developments on Fundamental Problems in Quantum Physics, edited by M. Ferrero and A. van der Merwe (Kluwer, Dordrecht, 1997)] and Hardy and co-workers [Phys. Rev. Lett. 79, 2755 (1997)] works only for nonmaximally entangled states and goes through for 50% of pairs at the most. A similar ladder proof for two spin-$1$ particles in a maximally entangled state is presented. In its simplest form, the proof goes through for 17% of pairs. An extended version works for 100% of pairs. The proof can be extended to any maximally entangled state of two spin-$s$ particles (with $s>~1)$.

DOI
10.1103/physreva.58.1687

Related papers

Ladder proof of nonlocality for two spin-half particles revisited

Jose Luis Cereceda

In this paper we extend the ladder proof of nonlocality without inequalities for two spin-half particles given by Boschi et al (Boschi D et al 1997 Phys. Rev. Lett. 79 2755) to the case in which the measurement settings of the apparatus measuring one of the particles are different from the measurement settings of the apparatus measuring the other particle. It is shown that, in any case, the proportion of particle pairs for which the contradiction with local realism goes through is maximized when the measurement settings are the same for each apparatus. Also we write down a Bell inequality for the experiment in question which is violated by quantum mechanics by an amount which is twice as much as the amount by which quantum mechanics violates the Bell inequality considered in the above paper by Boschi et al .

arXiv:quant-ph/0206015•Journal of Physics A Mathematical and General•Oct 15, 2002•1 citation

Quantum nonlocality for a three-particle nonmaximally entangled state without inequalities

Shi‐Biao Zheng

We show that it is possible to demonstrate quantum nonlocality for three particles in a nonmaximally entangled state without using inequality. The nonlocal effect might be much stronger than that which a two-particle nonmaximally entangled state can exhibit, as described by Hardy [Phys. Rev. Lett. 71, 1665 (1993)].

Physical Review A•Jul 18, 2002•37 citations

Hardy's Theorem for n Spin- s Particles in Entanglement

Wu Xiaohua, Zhao Yumin, Hsia Yuanfu

The Hardy's theorem [Phys. Rev. Lett. 71 (1993) 1665] is extended to n spin-s particles. As expected, the entangled states for these particles also admit a proof of nonlocality without using inequalities.

Communications in Theoretical Physics•Jul 30, 1998•0 citations

Nonlocality without inequalities for almost all entangled states for two particles

Sheldon Goldstein

We provide a streamlined proof of Hardy's theorem, that almost every entangled state for a pair of quantum particles admits a ``proof of nonlocality'' without inequalities. Moreover, our analysis covers a larger class of observables. Thus we also strengthen Hardy's assertion that the argument fails for maximally entangled states, such as the singlet state. At the same time, we formulate the argument in such a manner that the relations which must be satisfied for local hidden variables are entirely deterministic, making no reference whatsoever to probability, let alone probablistic inequalities.

Physical Review Letters•Mar 28, 1994•129 citations

Comment on "Quantum nonlocality for a three-particle nonmaximally entangled state without inequalities"

Jose Luis Cereceda

In a recent Brief Report, Zheng [S-B. Zheng, PRA 66, 014103 (2002)] has given a proof of nonlocality without using inequalities for three spin-1/2 particles in the nonmaximally entangled state |psi> = cosθ|+++> + i sinθ|-->. Here we show that Zheng's proof is not correct. Indeed it is the case that, for the experiment considered by Zheng, the only state that admits a nonlocality proof without inequalities is the maximally entangled state.

arXiv:quant-ph/0312046•Dec 5, 2003•0 citations

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
The ladder proof of nonlocality without inequalities for two spin-12\frac{1}{2}21​ particles proposed by Hardy [in New Developments on Fundamental Problems in Quantum Physics, edited by M. Ferrero and A. van der Merwe (Kluwer, Dordrecht, 1997)] and Hardy and co-workers [Phys. Rev. Lett. 79, 2755 (1997)] works only for nonmaximally entangled states and goes through for 50% of pairs at the most. A similar ladder proof for two spin-111 particles in a maximally entangled state is presented. In its simplest form, the proof goes through for 17% of pairs. An extended version works for 100% of pairs. The proof can be extended to any maximally entangled state of two spin-sss particles (with s> 1)s>~1)s> 1).
In this paper we extend the ladder proof of nonlocality without inequalities for two spin-half particles given by Boschi et al (Boschi D et al 1997 Phys. Rev. Lett. 79 2755) to the case in which the measurement settings of the apparatus measuring one of the particles are different from the measurement settings of the apparatus measuring the other particle. It is shown that, in any case, the proportion of particle pairs for which the contradiction with local realism goes through is maximized when the measurement settings are the same for each apparatus. Also we write down a Bell inequality for the experiment in question which is violated by quantum mechanics by an amount which is twice as much as the amount by which quantum mechanics violates the Bell inequality considered in the above paper by Boschi et al .
We provide a streamlined proof of Hardy's theorem, that almost every entangled state for a pair of quantum particles admits a ``proof of nonlocality'' without inequalities. Moreover, our analysis covers a larger class of observables. Thus we also strengthen Hardy's assertion that the argument fails for maximally entangled states, such as the singlet state. At the same time, we formulate the argument in such a manner that the relations which must be satisfied for local hidden variables are entirely deterministic, making no reference whatsoever to probability, let alone probablistic inequalities.