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Zhongguo kexue. Wulixue Lixue Tianwenxue

基于两光子偏振-空间模超纠缠态的高容量的量子秘密共享协议

Feng Liu, Yu‐Guang Yang

Published Sep 8, 2022• 3 citations
Publisher

Abstract

This paper proposes a feasible high-capacity tripartite quantum secret sharing protocol based on the two-photon polarization-spatial-mode hyperentangled state. Alice, the secret owner, prepares polarization-spatial-mode hyperentangled photon pairs and distributes them to two agents, Bob and Charlie. Using nonlocal complete Bell state analysis technology assisted by spatial mode entanglement, the two agents can collaborate to distinguish Alice’s Bell state in polarization degree of freedom. Only linear optical elements are needed to construct the agents’ measuring devices, which makes the protocol more feasible in experimental implementation. Compared with the existing quantum secret sharing protocols based on two-photon entanglement, this scheme does not need two-way quantum communication and has high capacity because it can transmit two bits of information with a polarization-spatial-mode hyperentangled photon pair. The proposed quantum secret sharing protocol is secure and reliable due to error correction and privacy amplification technology.

DOI
10.1360/sspma-2022-0198

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This paper proposes a feasible high-capacity tripartite quantum secret sharing protocol based on the two-photon polarization-spatial-mode hyperentangled state. Alice, the secret owner, prepares polarization-spatial-mode hyperentangled photon pairs and distributes them to two agents, Bob and Charlie. Using nonlocal complete Bell state analysis technology assisted by spatial mode entanglement, the two agents can collaborate to distinguish Alice’s Bell state in polarization degree of freedom. Only linear optical elements are needed to construct the agents’ measuring devices, which makes the protocol more feasible in experimental implementation. Compared with the existing quantum secret sharing protocols based on two-photon entanglement, this scheme does not need two-way quantum communication and has high capacity because it can transmit two bits of information with a polarization-spatial-mode hyperentangled photon pair. The proposed quantum secret sharing protocol is secure and reliable due to error correction and privacy amplification technology.
Quantum secret sharing (QSS) is a cornerstone of multi-party quantum information security. However, traditional QSS protocols are vulnerable to detector side-channel attacks. Measurement-device-independent QSS (MDI-QSS) elegantly resolves this by outsourcing measurements to an untrusted third party. Building upon this, we propose a measurement-deviceindependent dynamic quantum secret sharing (MDI-DQSS) scheme based on hyperentanglement. Our protocol leverages simultaneous entanglement in both polarization and spatial degrees of freedom, which enhances the channel capacity and improves the key generation rate. The scheme is designed for practical implementation, relying on single-photon states that are feasible to prepare and manipulate. We present the complete protocol, from state preparation and distribution to cooperative decoding, and provide a comprehensive security analysis demonstrating its robustness.
Imperfect single-photon detectors can lead to security flaws such as key information leakage and malicious information injection. We propose a three-party detector-device-independent quantum secret sharing protocol based on the single-photon Bell-state measurement and two-photon Bell-state distribution. Two agents develop connections among three communication parties by implementing spatial encoding of photons and performing single-photon Bell-state measurements in both polarization and spatial mode degrees of freedom, resulting in secret sharing among the three parties. This protocol can be implemented with linear optical elements and is simple for practical applications. Furthermore, we prove the security of the protocol and demonstrate its resistance to two common eavesdropping attacks.
Quantum secret sharing (QSS) is a typical multipartite cryptographic primitive, which is an important part of quantum communication network. Existing QSS protocols generally require basis selection and matching, which would increase the quantum resource consumption and classical communication round, and also face weak random security vulnerabilities. We propose an efficient hyperentanglement-based QSS protocol without the basis selection, in which the dealer and partners share a polarization-momentum hyperentangled Greenberger-Horne-Zeilinger (GHZ) state and encode keys in the polarization degree of freedom (DOF). The dealer decodes the transmitted keys relying on the nonlocal hyperentanglement-assisted polarization GHZ state analysis. Our QSS protocol is unconditionally secure in theory. We develop simulation method to estimate its performance in practical environment. Compared with the QSS based on the GHZ state, our protocol has several advantages. First, it does not require basis selection and can completely distinguish eight polarization GHZ states, which can improve the utilization rate of entanglement resources to 100%\%% and increase the key generation rate by an order of magnitude. Second, it only requires one round of classical communication, and thus can reduce key generation time by 69.4%\%%. Third, it can eliminate the weak random security vulnerabilities associated with the basis selection. Finally, our protocol only uses linear optical elements, which makes it practically feasible. Our QSS protocol has potential application in future quantum communication network.
We propose a scheme for the production of hyperentangled photon pairs as well as for the complete differentiation of 16 hyperentangled Bell states in both polarization and spatial-mode degrees of freedom using the quantum-dot cavity systems. This hyperentangled-Bell-state photon generation and the complete hyperentangled-Bell-state-analysis device can serve as crucial components of the high-capacity, long-distance quantum communication. We use the hyperentanglement quantum repeater as an example to show the application of this device. When the hyperentanglement quantum repeater operation is complete, two parties that are far from each other in quantum communication can share two Bell-state spin pairs simultaneously. By using numerical calculations we prove that the present scheme can both work in the weak- and strong-coupling regimes with current technology.
The semi-quantum key distribution protocol based on the hyperentanglement Bell state of polarization-spatial mode is presented in this paper. This protocol is utilized to share the session keys and construct key hierarchy of security systems in high capacity between the legitimate users securely. Different from the previous protocols, two quantum non-demolition detectors are constructed with cross-Kerr nonlinearities and different phase shifts for distinguishing the Bell states in spatial mode degree of freedom. Meanwhile, this protocol can improve the capacity and efficiency when the legitimate users share the session keys. And the technology of the hyperentanglement purification and hyperentanglement concentration can enhance the robustness and stability of this protocol. At last, this protocol proposed in this paper can withstand several kinds of attacks.
Bell-state analysis (BSA) is essential in quantum communication, but it is impossible to distinguish unambiguously the four Bell states in the polarization degree of freedom (DOF) of two-photon systems with only linear optical elements, except for the case in which the BSA is assisted with hyperentangled states, the simultaneous entanglement in more than one DOF. Here, we propose a scheme to distinguish completely the 16 hyperentangled Bell states in both the polarization and the spatial-mode DOFs of two-photon systems, by using the giant nonlinear optics in quantum dot-cavity systems. This scheme can be applied to increase the channel capacity of long-distance quantum communication based on hyperentanglement, such as entanglement swapping, teleportation, and superdense coding. We use hyperentanglement swapping as an example to show the application of this HBSA.