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Multi-system entanglement swapping for Bell states and Greenberger-Horne-Zeilinger states

Zhaoxu Ji, Peiru Fan, Huanguo Zhang

Published Nov 22, 2019• 2 citations
OpenAlex

Abstract

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.

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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 proposed two multiparty quantum secret sharing schemes based on n-particle Greenberger–Horne–Zeilinger-states (GHZ states), which are transformed from Einstein–Podolsky–Rosen pairs by entanglement swapping. In our schemes, the dealer imposes messages by performing local unitary operations (I, σ x, iσ y, σ z) on the n-particle GHZ state she holds, and the agents collaborate to deduce the dealer's messages by performing local unitary operations on their own qubit. The amount of dealer's secret message is positively related with the number of agents. The need of qubits is one-third less than the former schemes and, also, they can be reused for the next new round. The scheme (II) does not have to pre-share the code table, which increases the security without the risk of being stolen.
Since the first quantum secret sharing protocol based on Greenberger–Horne–Zeilinger (GHZ) states was presented by Hillery et al, dozens of quantum secret sharing protocols based on different entangled states (e.g. Bell states, d-level Bell states and GHZ states, etc) and product states have been developed. In this paper, we present a quantum secret sharing protocol, in which the genuinely maximally entangled six-qubit states, which was found recently by Borras et al, are used. An ordinary entangled state such as a Bell state or a GHZ state, etc can be used to share at most only one bit. However, according to our protocol, Alice can share three bits among three parties by a six-qubit state, which shows that our protocol is more efficient than any previous protocol.
Entanglement swapping is a key technology for multi-hop communication based on entanglement in quantum networks. However, the end-to-end delay of the traditional sequential entanglement swapping (SEQES) grows rapidly with the increase of network scale. To solve this problem, we first propose a low-delay multi-particle simultaneous entanglement swapping (SES) scheme to establish the remote four-particle Greenberger–Horne–Zeilinger (GHZ) channel states for the bidirectional teleportation of three-particle GHZ states, in which the intermediate nodes perform Bell state measurements, send the measurement results and the Bell state type to the user node Bob (or Alice) through classical channel simultaneously. Bob (or Alice) only needs to carry out a proper unitary operation according to the information he (or she) has received. Further, we put forward a hierarchical simultaneous entanglement swapping (HSES) scheme to reduce the classical information transmission cost, which is composed of level-1 SES and level-2 SES (schemes). The former is an inner segment SES, and the latter is an inter segments SES. Theoretical analysis and simulation results show the HSES can obtain the optimal performance tradeoff between end-to-end delay and classical cost.
Quantum secret sharing (QSS) is a crucial quantum cryptographic method that provides unconditional secu-rity through the principles of quantum mechanics and enables practical applications in information security and distributed computing. Many QSS protocols have been proposed based on various quantum properties and operations. In this study, we propose a new and efficient multiparty quantum secret sharing protocol that utilizes entanglement swapping with the Greenberger-Horne-Zeilinger (GHZ) state and introduces a novel structure to efficiently and securely distribute and recover secrets. Due to entanglement swapping, participants can entangle systems without directly interacting with each other, enhancing practical usage. Through GHZ entanglement swapping, initial particle states cannot be directly inferred. The proposed QSS protocol leverages this property to encode information among participants. To decode the secret, participants only require measuring particles on a GHZ basis to get the corresponding information without performing operations. Through security analysis, it is shown that any eavesdropper or dishonest participant will be detected. Efficiency analysis indicates that the proposed protocol substantially reduces costs and significantly enhances efficiency. As the number of participants increases, the resource consumption of the proposed protocol becomes much lower than that of other QSS protocols. In summary, the proposed protocol efficiently achieves unconditional security in QSS, ensuring the secure transmission and sharing of quantum information.
This Letter reports the first experimental demonstration of Greenberger-Horne-Zeilinger (GHZ) entanglement swapping. We start with three pairs of entangled photons. Upon projection of three single photons, each from an entangled pair, into a GHZ state, the other three originally independent photons are entangled in a GHZ state-creation of multiparticle entanglement without any direct interaction. This scheme may facilitate networks for quantum telephone exchange, multiparty quantum communication and distributed quantum computation.