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/9911039 · Physical Review A

Greenberger-Horne-Zeilinger paradoxes with symmetric multiport beam splitters

Marek Żukowski, Dagomir Kaszlikowski

Published May 1, 1999• 30 citations
arXivHTMLPDF

Abstract

In a gedanken experiment N particles in a generalized Greenberger-Horne-Zeilinger-(GHZ)-type beam-entangled state (each particle can be in one of M beams) are fed into N symmetric $2M$-port beam splitters (spatially separated). Correlation functions for such a process (using the Bell numbers value assignment approach) reveal a remarkable symmetry. For $N=M+1>~4$ a series of GHZ paradoxes are shown.

DOI
10.1103/physreva.59.3200

Related papers

Generating Greenberger-Horne-Zeilinger states using multiport splitters

Daniel Bhatti, Stefanie Barz

Symmetric multiport splitters are versatile tools in optical quantum information processing. They can be used for studying multiparticle scattering, for studying distinguishability and mixedness, and also for the generation of multipartite entangled quantum states. Here, we show that $N$-photon $N$-mode Greenberger-Horne-Zeilinger (GHZ) states can be generated using symmetric multiport beam splitters. Varying the input states' internal degrees of freedom and postselecting onto certain photon-number distributions allows the probabilistic generation of GHZ states with arbitrary photon numbers. We present two schemes, one for odd and one for even numbers of photons, to generate GHZ states using symmetric multiport splitters and compare them to a strategy utilizing a $2N$-port network as well as the standard postselection method.

arXiv:2302.00697•Physical Review A•Mar 30, 2023•10 citations

Greenberger-Horne-Zeilinger-state analyzer

Jian-Wei Pan, Anton Zeilinger

Using just polarizing beam splitters and half-wave plates, we present a practical experimental scheme, by which one can conveniently identify two of the three-particle Greenberger-Horne-Zeilinger (GHZ) states. The scheme can easily be generalized to the $N$-particle case. The GHZ-state analyzer is essential for multiparticle generalizations of quantum dense coding, quantum teleportation, and entanglement swapping.

Physical Review A•Mar 1, 1998•213 citations

Experimental test of the irreducible four-qubit Greenberger-Horne-Zeilinger paradox

Zu-En Su, Weidong Tang, Dian Wu +7 more

The paradox of Greenberger-Horne-Zeilinger (GHZ) disproves directly the concept of EPR elements of reality, based on the EPR correlations, in an all-versus-nothing way. A three-qubit experimental demonstration of the GHZ paradox was achieved nearly 20 years ago, followed by demonstrations for more qubits. Still, the GHZ contradictions underlying the tests can be reduced to a three-qubit one. We show an irreducible four-qubit GHZ paradox, and report its experimental demonstration. The bound of a three-setting-per-party Bell-GHZ inequality is violated by $7\ensuremath{\sigma}$. The fidelity of the GHZ state was around $81%$, and an entanglement witness reveals a violation of the separability threshold by $19\ensuremath{\sigma}$.

arXiv:1611.09990•Physical Review A•Mar 15, 2017•11 citations

Greenberger-Horne-Zeilinger Paradoxes from Qudit Graph States

Weidong Tang, Sixia Yu, C. H. Oh

One fascinating way of revealing quantum nonlocality is the all-versus-nothing test due to Greenberger, Horne, and Zeilinger (GHZ) known as the GHZ paradox. So far genuine multipartite and multilevel GHZ paradoxes are known to exist only in systems containing an odd number of particles. Here we shall construct GHZ paradoxes for an arbitrary number (greater than 3) of particles with the help of qudit graph states on a special kind of graphs, called GHZ graphs. Furthermore, based on the GHZ paradox arising from a GHZ graph, we derive a Bell inequality with two d-outcome observables for each observer, whose maximal violation attained by the corresponding graph state, and a Kochen-Specker inequality testing the quantum contextuality in a state-independent fashion.

arXiv:1206.2718•Physical Review Letters•Mar 6, 2013•40 citations

Nonlocality of three-qubit Greenberger-Horne-Zeilinger–symmetric states

Biswajit Paul, Kaushiki Mukherjee, Debasis Sarkar

Mixed states appear naturally in experiment over pure states. So for studying different notions of nonlocality and their relation with entanglement in realistic scenarios, one needs to consider mixed states. In a recent paper [Phys. Rev. Lett. 108, 020502 (2012)], a complete characterization of entanglement of an entire class of mixed three-qubit states with the same symmetry as the Greenberger-Horne-Zeilinger state, known as GHZ-symmetric states, has been achieved. In this paper we investigate different notions of nonlocality of the same class of states. By finding the analytical expressions of maximum violation value of most efficient Bell inequalities we obtain the conditions of standard nonlocality and genuine nonlocality of this class of states. Also the relation between entanglement and nonlocality is discussed for this class of states. Interestingly, genuine entanglement of GHZ-symmetric states is necessary to reveal standard nonlocality. However, it is not sufficient to exploit the same.

arXiv:1608.04140•Physical Review A•Sep 2, 2016•15 citations

Heralding Higher-Dimensional Bell and Greenberger–Horne–Zeilinger states using multiport splitters

Daniel Bhatti, Stefanie Barz

Abstract One of the most important resources for quantum optical experiments and applications are on-demand highly entangled multiphoton quantum states. A promising way of generating them is heralding entanglement generation at a high rate from letting independent photons interfere. However, such schemes often work for a specific internal degree of freedom of the interfering photons only. Going to higher numbers of entangled photons, the success probabilities decrease while the number of necessary resources, e.g. auxiliary photons and optical elements, increases. To make probabilistic schemes feasible also for larger quantum states, it is therefore important to find resource-efficient generation schemes with high success probabilities. In this work, we introduce easily implementable schemes to herald qubit Greenberger–Horne–Zeilinger (GHZ) states, higher-dimensional Bell states and higher-dimensional three-party GHZ states. Our schemes solely rely on multiphoton interference, i.e. they can be adjusted to work for arbitrary degrees of freedom. Furthermore, they demonstrate high success probabilities and need comparably few auxiliary photons.

arXiv:2408.08473•New Journal of Physics•Feb 21, 2025•8 citations
In a gedanken experiment N particles in a generalized Greenberger-Horne-Zeilinger-(GHZ)-type beam-entangled state (each particle can be in one of M beams) are fed into N symmetric 2M2M2M-port beam splitters (spatially separated). Correlation functions for such a process (using the Bell numbers value assignment approach) reveal a remarkable symmetry. For N=M+1> 4N=M+1>~4N=M+1> 4 a series of GHZ paradoxes are shown.
Symmetric multiport splitters are versatile tools in optical quantum information processing. They can be used for studying multiparticle scattering, for studying distinguishability and mixedness, and also for the generation of multipartite entangled quantum states. Here, we show that NNN-photon NNN-mode Greenberger-Horne-Zeilinger (GHZ) states can be generated using symmetric multiport beam splitters. Varying the input states' internal degrees of freedom and postselecting onto certain photon-number distributions allows the probabilistic generation of GHZ states with arbitrary photon numbers. We present two schemes, one for odd and one for even numbers of photons, to generate GHZ states using symmetric multiport splitters and compare them to a strategy utilizing a 2N2N2N-port network as well as the standard postselection method.
Using just polarizing beam splitters and half-wave plates, we present a practical experimental scheme, by which one can conveniently identify two of the three-particle Greenberger-Horne-Zeilinger (GHZ) states. The scheme can easily be generalized to the NNN-particle case. The GHZ-state analyzer is essential for multiparticle generalizations of quantum dense coding, quantum teleportation, and entanglement swapping.
The paradox of Greenberger-Horne-Zeilinger (GHZ) disproves directly the concept of EPR elements of reality, based on the EPR correlations, in an all-versus-nothing way. A three-qubit experimental demonstration of the GHZ paradox was achieved nearly 20 years ago, followed by demonstrations for more qubits. Still, the GHZ contradictions underlying the tests can be reduced to a three-qubit one. We show an irreducible four-qubit GHZ paradox, and report its experimental demonstration. The bound of a three-setting-per-party Bell-GHZ inequality is violated by $7\ensuremath{\sigma}$. The fidelity of the GHZ state was around 8181%81, and an entanglement witness reveals a violation of the separability threshold by $19\ensuremath{\sigma}$.
One fascinating way of revealing quantum nonlocality is the all-versus-nothing test due to Greenberger, Horne, and Zeilinger (GHZ) known as the GHZ paradox. So far genuine multipartite and multilevel GHZ paradoxes are known to exist only in systems containing an odd number of particles. Here we shall construct GHZ paradoxes for an arbitrary number (greater than 3) of particles with the help of qudit graph states on a special kind of graphs, called GHZ graphs. Furthermore, based on the GHZ paradox arising from a GHZ graph, we derive a Bell inequality with two d-outcome observables for each observer, whose maximal violation attained by the corresponding graph state, and a Kochen-Specker inequality testing the quantum contextuality in a state-independent fashion.
Mixed states appear naturally in experiment over pure states. So for studying different notions of nonlocality and their relation with entanglement in realistic scenarios, one needs to consider mixed states. In a recent paper [Phys. Rev. Lett. 108, 020502 (2012)], a complete characterization of entanglement of an entire class of mixed three-qubit states with the same symmetry as the Greenberger-Horne-Zeilinger state, known as GHZ-symmetric states, has been achieved. In this paper we investigate different notions of nonlocality of the same class of states. By finding the analytical expressions of maximum violation value of most efficient Bell inequalities we obtain the conditions of standard nonlocality and genuine nonlocality of this class of states. Also the relation between entanglement and nonlocality is discussed for this class of states. Interestingly, genuine entanglement of GHZ-symmetric states is necessary to reveal standard nonlocality. However, it is not sufficient to exploit the same.
Abstract One of the most important resources for quantum optical experiments and applications are on-demand highly entangled multiphoton quantum states. A promising way of generating them is heralding entanglement generation at a high rate from letting independent photons interfere. However, such schemes often work for a specific internal degree of freedom of the interfering photons only. Going to higher numbers of entangled photons, the success probabilities decrease while the number of necessary resources, e.g. auxiliary photons and optical elements, increases. To make probabilistic schemes feasible also for larger quantum states, it is therefore important to find resource-efficient generation schemes with high success probabilities. In this work, we introduce easily implementable schemes to herald qubit Greenberger–Horne–Zeilinger (GHZ) states, higher-dimensional Bell states and higher-dimensional three-party GHZ states. Our schemes solely rely on multiphoton interference, i.e. they can be adjusted to work for arbitrary degrees of freedom. Furthermore, they demonstrate high success probabilities and need comparably few auxiliary photons.