We introduce a class of multi-particle Greenberger-Horne-Zeilinger (GHZ) states, and study entanglement swapping between two qubit systems for Bell states and for the class of GHZ states, respectively. We generalize the bi-system entanglement swapping of Bell states and multi-particle GHZ states to any number of qubit systems. We further study the entanglement swapping schemes between any number of Bell states and between any number of the introduced GHZ states in a detailed way, and propose the schemes that can generate two identical GHZ states. We illustrate the applications of such schemes in quantum information processing by proposing quantum protocols for quantum key distribution, quantum secret sharing and quantum private comparison.We introduce a class of multi-particle Greenberger-Horne-Zeilinger (GHZ) states, and study entanglement swapping between two qubit systems for Bell states and for the class of GHZ states, respectively. We generalize the bi-system entanglement swapping of Bell states and multi-particle GHZ states to any number of qubit systems. We further study the entanglement swapping schemes between any number of Bell states and between any number of the introduced GHZ states in a detailed way, and propose the schemes that can generate two identical GHZ states. We illustrate the applications of such schemes in quantum information processing by proposing quantum protocols for quantum key distribution, quantum secret sharing and quantum private comparison.

Nov 22, 20192 citations

Hybrid entanglement swapping of photons: Creating the orbital angular momentum Bell states and Greenberger-Horne-Zeilinger states

Lixiang Chen, Weilong She

Twisted photons offer a high-dimensional Hilbert space with the degree of freedom of orbital angular momentum (OAM). Entanglement swapping allows entangling photons that never interact. We report in this paper the hybrid entanglement swapping from multiphoton spin-entangled states to multiphoton OAM entangled states with the aid of $N$ -pair hybrid spin-OAM entangled photons. Our scheme provides a feasible method for creating the two-photon OAM Bell states $(N=2)$ or multiphoton multidimensional OAM Greenberger-Horne-Zeilinger states $(N\ensuremath{\ge}3)$. We highlight the advantage of multiparticle, multidimensional entangled states in some applications of quantum information protocols.Twisted photons offer a high-dimensional Hilbert space with the degree of freedom of orbital angular momentum (OAM). Entanglement swapping allows entangling photons that never interact. We report in this paper the hybrid entanglement swapping from multiphoton spin-entangled states to multiphoton OAM entangled states with the aid of $N$-pair hybrid spin-OAM entangled photons. Our scheme provides a feasible method for creating the two-photon OAM Bell states $(N=2)$ or multiphoton multidimensional OAM Greenberger-Horne-Zeilinger states $(N\ensuremath{\ge}3)$. We highlight the advantage of multiparticle, multidimensional entangled states in some applications of quantum information protocols.

Physical Review AJan 14, 201121 citations

Swapped entanglement in high-dimensional quantum systems

S. M. Zangi, Chitra Shukla, Khalid Naseer +1 more

arXiv:2508.00634Quantum Information ProcessingJul 23, 20261 citation

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.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 ANov 17, 20035 citations

Entanglement classification of symmetric N-qubit States

Thierry Bastin, Stéphanie Krins, Pierre Mathonet +3 more

Jan 1, 20090 citations

N

-pair hybrid spin-OAM entangled photons. Our scheme provides a feasible method for creating the two-photon OAM Bell states

(N=2)

or multiphoton multidimensional OAM Greenberger-Horne-Zeilinger states $(N\ensuremath{\ge}3)$. We highlight the advantage of multiparticle, multidimensional entangled states in some applications of quantum information protocols.