High-dimensional measurement-device-independent quantum secure direct communication

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High-dimensional measurement-device-independent quantum secure direct communication Lu Liu1 · Jia-Lei Niu1 · Chen-Rui Fan2 · Xue-Ting Feng2 · Chuan Wang2 Received: 5 July 2020 / Accepted: 21 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020

Abstract Quantum secure direct communication is an important communication mode of quantum communications. Its development and application are mainly limited by the channel capacity and channel loss. Here, in this paper, a high-dimensional measurement-device-independent quantum secure direct communication protocol is proposed. The quantum information is encoded on the spatial mode of the photons which enlarges the coding Hilbert space and results in the high efficiency, feasibility with existing technique, and tolerance of channel noise. Based on realistic experimental parameters, the efficiency of communications is analytically derived and numerically discussed. Keywords High-dimension · Measurement-device-independent · Quantum secure direct communication

1 Introduction The security of information transmission is becoming ever more important in modern society. With the development of computation power, especially the quantum computer, classic cryptography is unable to finish the task of secure information transmission. On the other hand, quantum cryptography offers unconditional security of communications based on the laws of quantum physics. During the past decades, quantum communications has attracted intensive attention and made rapid progress, such as in the field of quantum key distribution (QKD) [1–11], quantum secret sharing [12,13], and quantum secure direct communication (QSDC) [14]. Specifically, QKD is to generate the random keys between communication parties, while QSDC is used for direct transmission of secret information. Among these branches, QSDC

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Chuan Wang [email protected]

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School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

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School of Artificial Intelligence, Beijing Normal University, Beijing 100875, China 0123456789().: V,-vol

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is characterized by eliminating the security loopholes of the process of key storage, distribution, and transmission, which attracts intense research interest [15–19]. The first QSDC protocol was proposed by Long et al. [14]. Later in 2003, exploiting the entangled quantum state, the two-step QSDC protocol was proposed [15]. Moreover, Deng et al. also put forward a QSDC protocol-based on single photons [20]. The high-dimensional QSDC protocol with superdense coding is also presented [21]. The main obstacle of the experiment is the quantum storage of photons during communications. In 2016, Hu et al. realized the first QSDC experiment using single photons without quantum storage [22]. Later, the QSDC using atomic ensembles for storage is implemented [16]. Meanwhile, the fiber-based QSDC and long-distance QSDC have been realized [23]. Recently, the distance of QSDC has been increased to 1.5 km, with a bit rate