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

Physical Review Letters

Nonlocality without inequalities for almost all entangled states for two particles

Sheldon Goldstein

Published Mar 28, 1994• 129 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.72.1951

Related papers

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

Ladder proof of nonlocality without inequalities and without probabilities

Adán Cabello

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 $s>~1)$.

arXiv:quant-ph/9712055•Physical Review A•Sep 1, 1998•18 citations

Bell's Theorem Without Inequalitites for a Maximally Entangled State

LiMing, W.

A proof of Bell's theorem without inequalities for two maximally entangled particles is proposed using the technique of quantum teleportation. It follows Hardy's arguments for a non-maximally entangled state with the help of two auxiliary particles without correlation. The present proof can be tested by measurements with 100% probability.

arXiv:quant-ph/0204055•Apr 10, 2002•0 citations

Quantum perfect correlations and Hardy's nonlocality theorem

Jose Luis Cereceda

In this paper the failure of Hardy's nonlocality proof for the class of maximally entangled states is considered. A detailed analysis shows that the incompatibility of the Hardy equations for this class of states physically originates from the fact that the existence of quantum perfect correlations for the three pairs of two-valued observables (D_11,D_21), (D_11,D_22) and (D_12,D_21) [in the sense of having with certainty equal (different) readings for a joint measurement of any one of the pairs (D_11,D_21), (D_11,D_22), and (D_12,D_21)], necessarily entails perfect correlation for the pair of observables (D_12,D_22) [in the sense of having with certainty equal (different) readings for a joint measurement of the pair (D_12,D_22)]. Indeed, the set of these four perfect correlations is found to satisfy the CHSH inequality, and then no violations of local realism will arise for the maximally entangled state as far as the four observables D_ij, i,j = 1,2, are concerned. The connection between this fact and the impossibility for the quantum mechanical predictions to give the maximum possible theoretical violation of the CHSH inequality is pointed out. Moreover, it is generally proved that the fulfillment of all the Hardy nonlocality conditions necessarily entails a violation of the resulting CHSH inequality. The largest violation of this latter inequality is determined.

arXiv:quant-ph/9908039•Aug 12, 1999•0 citations

Nonlocality without inequality for almost all two-qubit entangled states based on Cabello’s nonlocality argument

Samir Kunkri, Sujit K. Choudhary, Ali Ahanj +1 more

Here we deal with a nonlocality argument proposed by Cabello, which is more general than Hardy's nonlocality argument, but still maximally entangled states do not respond. However, for most of the other entangled states, maximum probability of success of this argument is more than that of the Hardy's argument.

arXiv:quant-ph/0512025•Physical Review A•Feb 24, 2006•22 citations

Nonlocality without inequalities has not been proved for maximally entangled states

Adán Cabello

Two approaches to extend Hardy's proof of nonlocality without inequalities to maximally entangled states of bipartite two-level systems are shown to fail. On one hand, it is shown that the proof of Wu and co-workers [Phys. Rev. A 53, R1927 (1996)] uses an effective state which is not maximally entangled. On the other hand, it is demonstrated that Hardy's proof cannot be generalized by the replacement of one of the four von Neumann measurements involved in the original proof by a generalized measurement to unambiguously discriminate between nonorthogonal states.

arXiv:quant-ph/9911023•Physical Review A•Jan 18, 2000•7 citations
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.
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 the failure of Hardy's nonlocality proof for the class of maximally entangled states is considered. A detailed analysis shows that the incompatibility of the Hardy equations for this class of states physically originates from the fact that the existence of quantum perfect correlations for the three pairs of two-valued observables (D_11,D_21), (D_11,D_22) and (D_12,D_21) [in the sense of having with certainty equal (different) readings for a joint measurement of any one of the pairs (D_11,D_21), (D_11,D_22), and (D_12,D_21)], necessarily entails perfect correlation for the pair of observables (D_12,D_22) [in the sense of having with certainty equal (different) readings for a joint measurement of the pair (D_12,D_22)]. Indeed, the set of these four perfect correlations is found to satisfy the CHSH inequality, and then no violations of local realism will arise for the maximally entangled state as far as the four observables D_ij, i,j = 1,2, are concerned. The connection between this fact and the impossibility for the quantum mechanical predictions to give the maximum possible theoretical violation of the CHSH inequality is pointed out. Moreover, it is generally proved that the fulfillment of all the Hardy nonlocality conditions necessarily entails a violation of the resulting CHSH inequality. The largest violation of this latter inequality is determined.
Two approaches to extend Hardy's proof of nonlocality without inequalities to maximally entangled states of bipartite two-level systems are shown to fail. On one hand, it is shown that the proof of Wu and co-workers [Phys. Rev. A 53, R1927 (1996)] uses an effective state which is not maximally entangled. On the other hand, it is demonstrated that Hardy's proof cannot be generalized by the replacement of one of the four von Neumann measurements involved in the original proof by a generalized measurement to unambiguously discriminate between nonorthogonal states.