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

Macroscopic boson states exhibiting the Greenberger-Horne-Zeilinger contradiction with local realism

M. D. Reid, William J. Munro

Published Aug 17, 1992• 36 citations
Publisher

Abstract

It is shown that the recent Greenberger-Horne-Zeilinger ``all or nothing'' contradiction of quantum mechanics with local realism can be exhibited on a macroscopic scale where a large number of particles are incident on each analyzer. We present a formulation of the all or nothing paradox in terms of boson fields, and suggest how the paradox might be realized using a correlated photon triplet. The suggested experiment might be readily extended to test, for the first time to our knowledge, quantum mechanics against local realism for situations of more than one quanta per wave packet incident on each measurement apparatus.

DOI
10.1103/physrevlett.69.997

Related papers

Characterizing Greenberger-Horne-Zeilinger Correlations in Nondegenerate Parametric Oscillation via Phase Measurements

William J. Munro, Gerard J Milburn

We present a potential realization of the Greenberger-Horne-Zeilinger ``all or nothing'' contradiction of quantum mechanics with local realism using phase measurement techniques in a simple photon number triplet. Such a triplet could be generated using nondegenerate parametric oscillation.

arXiv:quant-ph/9810075•Physical Review Letters•Nov 16, 1998•21 citations

Phase measurement tests of quantum mechanics

William J. Munro, Gerard J Milburn

We present a potential realization of the Greenberger, Horne and Zeilinger “all or nothing” contradiction of quantum mechanics with local realism using phase measurement techniques in a simple photon number triplet.

Mysteries, Puzzles, and Paradoxes in Quantum Mechanics•Jan 1, 1999•0 citations

Proposal for a mesoscopic cavity QED realization of the Greenberger-Horne-Zeilinger state

Christopher C. Gerry

A proposal is made for obtaining a mesoscopic realization of the Greenberger-Horne-Zeilinger (GHZ) "all or nothing" contradiction between quantum mechanics and local realism in the context of cavity QED. The proposed experiment involves three separated micromaser cavities, each initially prepared in a coherent state, which are then entangled by dispersive atom-field interactions followed by selective ionization of a single atom that has passed through all three cavities. The cavities are then probed individually by single atoms manipulated to obtain a measurement of the parity of the cavity fields. Using an isomorphism between coherent-state cavity fields and a spin-\textonehalf{} system, we show how this experiment gives rise to violations of local realism in the manner of GHZ.

Physical Review A•Oct 1, 1996•86 citations

General proof of the Greenberger-Horne-Zeilinger theorem

Zeqian Chen

It is proved that all states of three spin-$\frac{1}{2}$ particles exhibiting an ``all versus nothing'' contradiction between quantum mechanics and the local realism of Einstein, Podolsky, and Rosen are exactly the Greenberger-Horne-Zeilinger (GHZ) states and the states obtained from them by local unitary transformations. The proof is obtained by showing that there are at most four elements (except for a different sign) in a set of mutually commuting nonlocal spin observables in the three-qubit system and using the certain algebraic properties that Pauli's matrices satisfy. We show that only does such a set of four nonlocal spin observables present a Greenberger-Horne-Zeilinger-Mermin-like argument. This also reveals the equivalence between the GHZ theorem and maximal violation of the Bell inequality.

Physical Review A•Sep 24, 2004•1 citation

New Tests of Macroscopic Local Realism using Continuous Variable Measurements

M. D. Reid

We show that quantum mechanics predicts an Einstein-Podolsky-Rosen paradox (EPR), and also a contradiction with local hidden variable theories, for photon number measurements which have limited resolving power, to the point of imposing an uncertainty in the photon number result which is macroscopic in absolute terms. We show how this can be interpreted as a failure of a new, very strong premise, called macroscopic local realism. We link this premise to the Schrodinger-cat paradox. Our proposed experiments ensure all fields incident on each measurement apparatus are macroscopic. We show that an alternative measurement scheme corresponds to balanced homodyne detection of quadrature phase amplitudes. The implication is that where either EPR correlations or failure of local realism is predicted for continuous variable (quadrature phase amplitude) measurements, one can perform a modified experiment which would lead to conclusions about the much stronger premise of macroscopic local realism.

arXiv:quant-ph/0101050•Jan 12, 2001•0 citations

Greenberger-Horne-Zeilinger theorem cannot be extended to a Bell state

Zeqian Chen

The Greenberger-Horne-Zeilinger (GHZ) theorem exhibits an ``all versus nothing'' contradiction between Ernstein, Podelsky, and Rosen's local realism and quantum mechanics by using a maximally entangled state of three qubits. However, it is shown in this paper that no extension of GHZ's proof is possible for any entangled state of two qubits, including Bell states. The proof is obtained by showing the fact that there are no more than three distinct elements (except for a different sign) in a set of mutually commuting nonlocal spin observables of two qubits. This also leads to a generic setup of the Kochen-Specker theorem for the two-qubit system.

Physical Review A•Nov 17, 2003•5 citations
It is shown that the recent Greenberger-Horne-Zeilinger ``all or nothing'' contradiction of quantum mechanics with local realism can be exhibited on a macroscopic scale where a large number of particles are incident on each analyzer. We present a formulation of the all or nothing paradox in terms of boson fields, and suggest how the paradox might be realized using a correlated photon triplet. The suggested experiment might be readily extended to test, for the first time to our knowledge, quantum mechanics against local realism for situations of more than one quanta per wave packet incident on each measurement apparatus.
A proposal is made for obtaining a mesoscopic realization of the Greenberger-Horne-Zeilinger (GHZ) "all or nothing" contradiction between quantum mechanics and local realism in the context of cavity QED. The proposed experiment involves three separated micromaser cavities, each initially prepared in a coherent state, which are then entangled by dispersive atom-field interactions followed by selective ionization of a single atom that has passed through all three cavities. The cavities are then probed individually by single atoms manipulated to obtain a measurement of the parity of the cavity fields. Using an isomorphism between coherent-state cavity fields and a spin-\textonehalf{} system, we show how this experiment gives rise to violations of local realism in the manner of GHZ.
It is proved that all states of three spin-12\frac{1}{2}21​ particles exhibiting an ``all versus nothing'' contradiction between quantum mechanics and the local realism of Einstein, Podolsky, and Rosen are exactly the Greenberger-Horne-Zeilinger (GHZ) states and the states obtained from them by local unitary transformations. The proof is obtained by showing that there are at most four elements (except for a different sign) in a set of mutually commuting nonlocal spin observables in the three-qubit system and using the certain algebraic properties that Pauli's matrices satisfy. We show that only does such a set of four nonlocal spin observables present a Greenberger-Horne-Zeilinger-Mermin-like argument. This also reveals the equivalence between the GHZ theorem and maximal violation of the Bell inequality.
We show that quantum mechanics predicts an Einstein-Podolsky-Rosen paradox (EPR), and also a contradiction with local hidden variable theories, for photon number measurements which have limited resolving power, to the point of imposing an uncertainty in the photon number result which is macroscopic in absolute terms. We show how this can be interpreted as a failure of a new, very strong premise, called macroscopic local realism. We link this premise to the Schrodinger-cat paradox. Our proposed experiments ensure all fields incident on each measurement apparatus are macroscopic. We show that an alternative measurement scheme corresponds to balanced homodyne detection of quadrature phase amplitudes. The implication is that where either EPR correlations or failure of local realism is predicted for continuous variable (quadrature phase amplitude) measurements, one can perform a modified experiment which would lead to conclusions about the much stronger premise of macroscopic local realism.
The Greenberger-Horne-Zeilinger (GHZ) theorem exhibits an ``all versus nothing'' contradiction between Ernstein, Podelsky, and Rosen's local realism and quantum mechanics by using a maximally entangled state of three qubits. However, it is shown in this paper that no extension of GHZ's proof is possible for any entangled state of two qubits, including Bell states. The proof is obtained by showing the fact that there are no more than three distinct elements (except for a different sign) in a set of mutually commuting nonlocal spin observables of two qubits. This also leads to a generic setup of the Kochen-Specker theorem for the two-qubit system.