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Quantum Information Processing

Quantum secure direct communication with heralded superposition source of squeezed states

Jinyu Wang, Jia‐Wei Ying, Qi Zhang, Shi‐Pu Gu, Xing-Fu Wang, Lan Zhou, Yu‐Bo Sheng

Published Apr 18, 2026• 0 citations
Publisher

Abstract

Abstract Quantum secure direct communication (QSDC) promises unconditional security for direct information transmission without pre-shared keys. However, practical implementations using weak coherent sources face critical challenges from device imperfections, such as emitting vacuum states and multiphoton states. Here, we introduce a heralded QSDC protocol leveraging squeezed-state superposition in a cross-Kerr nonlinear medium, where single-mode squeezed states interfere with coherent states to generate superposition states via post-measurement selection. We have considered three detector models to analyze the heralding performance of light sources under different conditions, including the ideal photon number detector, the practical photon number detector, and the practical photon detector. Our proposed protocol dramatically reduces the vacuum state ratio compared to weak coherent pulse sources, and the multiphoton ratio is still maintained at a low level, significantly enhancing the security information capacity and the maximum secure communication distance. We perform numerical simulations and compare our protocol with the optical single-photon-based QSDC protocol. At 7.5 km with an average photon number of 0.01, the security information capacity improves by 13.42 times, 12.20 times, and 8.64 times for three detector models. Extending to 17.5 km, these gains will be to 277.59 times, 251.58 times, and 172.91 times. Our work provides a robust framework for high-capacity, long-distance, secure quantum communication systems. PACS numbers: 03.67.Pp, 03.67.Hk, 03.65.Ud

DOI
10.1007/s11128-026-05171-8

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Abstract Quantum secure direct communication (QSDC) promises unconditional security for direct information transmission without pre-shared keys. However, practical implementations using weak coherent sources face critical challenges from device imperfections, such as emitting vacuum states and multiphoton states. Here, we introduce a heralded QSDC protocol leveraging squeezed-state superposition in a cross-Kerr nonlinear medium, where single-mode squeezed states interfere with coherent states to generate superposition states via post-measurement selection. We have considered three detector models to analyze the heralding performance of light sources under different conditions, including the ideal photon number detector, the practical photon number detector, and the practical photon detector. Our proposed protocol dramatically reduces the vacuum state ratio compared to weak coherent pulse sources, and the multiphoton ratio is still maintained at a low level, significantly enhancing the security information capacity and the maximum secure communication distance. We perform numerical simulations and compare our protocol with the optical single-photon-based QSDC protocol. At 7.5 km with an average photon number of 0.01, the security information capacity improves by 13.42 times, 12.20 times, and 8.64 times for three detector models. Extending to 17.5 km, these gains will be to 277.59 times, 251.58 times, and 172.91 times. Our work provides a robust framework for high-capacity, long-distance, secure quantum communication systems. PACS numbers: 03.67.Pp, 03.67.Hk, 03.65.Ud
Quantum secure direct communications (QSDC) can directly transmit secret messages through a quantum channel without keys. The imperfect photon source is a major obstacle for QSDC's practical implementation. The unwanted vacuum state and multiphoton components emitted from imperfect photon source largely reduce QSDC's secrecy message capacity and even threaten its security. In the paper, we propose a high-efficient passive decoy-state QSDC protocol with the heralded single-photon source (HSPS). We adopt a spontaneous parametric down-conversion source to emit entangled photon pairs in two spatial modes. By detecting the photons in one of the two correlated spatial modes, we can infer the photon-number distribution of the other spatial mode. Meanwhile, our protocol allows a simple passive preparation of the signal states and decoy state. The HSPS can effectively reduce the probability of vacuum state and increase QSDC's secrecy message capacity. Meanwhile, the passive decoy-state method can simplify the experimental operations and enhance QSDC's robustness against the third-party side-channel attacks. Under the communication distance of 10 km, the secrecy message capacity of our QSDC protocol can achieve 81.85 times with average photon number of 0.1 and 12.79 times with average photon number of 0.01 of that in the original single-photon-based QSDC protocol without the HSPS. Our QSDC protocol has longer maximal communication distance about 17.975 km with average photon number of 0.01. Our work serves as a major step toward the further development of practical passive decoy-state QSDC systems.
Quantum secure direct communications (QSDC) can directly transmit secret messages through a quantum channel without keys. The imperfect photon source is a major obstacle for QSDC's practical implementation. The unwanted vacuum state and multiphoton components emitted from imperfect photon source largely reduce QSDC's secrecy message capacity and even threaten its security. In the paper, we propose a high-efficient passive decoy-state QSDC protocol with the heralded single-photon source (HSPS). We adopt a spontaneous parametric down-conversion source to emit entangled photon pairs in two spatial modes. By detecting the photons in one of the two correlated spatial modes, we can infer the photon-number distribution of the other spatial mode. Meanwhile, our protocol allows a simple passive preparation of the signal states and decoy state. The HSPS can effectively reduce the probability of vacuum state and increase QSDC's secrecy message capacity. Meanwhile, the passive decoy-state method can simplify the experimental operations and enhance QSDC's robustness against the third-party side-channel attacks. Under the communication distance of 10 km, the secrecy message capacity of our QSDC protocol can achieve 81.85 times with average photon number of 0.1 and 12.79 times with average photon number of 0.01 of that in the original single-photon-based QSDC protocol without the HSPS. Our QSDC protocol has longer maximal communication distance about 17.975 km with average photon number of 0.01. Our work serves as a major step toward the further development of practical passive decoy-state QSDC systems.
Abstract Quantum secure direct communication (QSDC) enables the direct transmission of confidential messages without pre-establishing a secret key. Device independence (DI) can further enhance its practical security against untrusted devices. However, existing DI-QSDC protocols rely on a single Clauser–Horne–Shimony–Holt inequality, which severely limits both the achievable communication distance and the secret message capacity, while the detection loophole remains open in DI-QSDC. To overcome these limitations, we propose a one-sided DI-QSDC protocol based on single-photon sources and heralded entanglement. The protocol combines entanglement distribution, loss-tolerant steering-based security verification, and measurement-DI communication verification and decoding. We employ the Navascués–Pironio–Acín hierarchy based semidefinite programming relaxations to evaluate the secret message capacity. Numerical simulations show that our protocol extends communication distances by factors of 5.6 and 32.2, and improves the practical secure communication efficiency by factors of 1.8 and 1102.5, compared to single-photon-source-based DI-QSDC and SPDC-based DI-QSDC, respectively.
As a novel paradigm in quantum communication, quantum secure direct communication (QSDC) enables secure, reliable, and deterministic information transmission, leveraging the principles of quantum mechanics. One-photon-interference QSDC is particularly attractive because it mitigates the vulnerabilities in measurement devices while extending transmission distances. In this paper, we propose a high-dimensional one-photon-interference QSDC protocol that exploits the advantages of high-dimensional encoding in the phase of weak coherent pluses to further enhance transmission distances and improve secrecy channel capacity. The security of this protocol is analyzed using quantum wiretap channel theory, and its resistance to common quantum threats is discussed. Numerical simulations demonstrate that our protocol outperforms its predecessor in terms of its secrecy capacity and extends the maximum communication distance achievable up to 494 km, which is over 13% longer than the two-dimensional case, effectively doubling the transmission length of traditional protocols. These improvements highlight the protocol's potential for use in quantum communication applications in this era of frequent data breaches and information leaks.
Quantum secure direct communication (QSDC) is a recently developed practical solution, which transmits secret messages between legitimate parties, without setting up a cryptographic key. The QSDC protocols are mainly classified into entanglement-based and single photon-based approaches. Their security has been analyzed using Wyner's wiretap channel theory, and their secrecy capacity has been calculated [1]. Hitherto, QSDC protocols have been implemented on optical fiber and free-space channels, all in discrete-variable (DV) encoding that employs single-photon detectors [1]–[2]. However, the implementation of continuous-variable (CV) QSDC, in which the keys are encoded into the quadratures of quantized electromagnetic fields (e.g., coherent states) and detected via homodyne techniques, is preferred due to: its lower costs, excellent integrability with existing optical communication systems, easy implementation from state preparation to measurement, and fast experimental realization. Furthermore, it has been proved that CV-QSDC protocols using squeezed states show higher tolerance in purely lossy channels and enhanced robustness against highly noisy ones, as well [3]. Nevertheless, none of the CV-QSDC protocols employing either coherent or squeezed quantum states have been implemented yet.
Current quantum secure direct communication (QSDC) protocols guarantee communication security by estimating the error rates of photons in the X and Z bases. This take the reference frame calibration between communicating parties as a necessary prerequisite. However, in mobile communications scenarios, achieving continuous and accurate reference frame calibration poses significant challenges. To address this issue, this paper proposes a reference-frame-independent (RFI) QSDC protocol. This protocol only requires ensuring the calibration accuracy of one direction of the reference frame, while allowing a misalignment angle βββ in the other two directions. To improve the protocol's robustness against reference frame fluctuations, we introduce a βββ-independent parameter C into the security analysis framework and rederive the protocol's security bounds. Additionally, we construct a system model and optimize the pulse intensity of the signal states, enabling the protocol to achieve optimal performance under each level of channel attenuation. At an attenuation of 10 dB (corresponding to a communication distance of 25 km), the secrecy message capacities for $β= 0^{ \circ} $ and $45^{ \circ} $ are 8.765×10−68.765 \times10^{-6}8.765×10−6 bit/pulse and 4.150×10−64.150 \times10^{-6}4.150×10−6 bit/pulse, respectively. Compared with the single-photon-based QSDC, the communication distance of the protocol proposed in this paper is significantly extended. When $β= 0^{ \circ} $ and $45^{ \circ} $, the maximum transmission distances of the RFI QSDC protocol are 27.875 km and 26.750 km, which is about 155.9 % and 149.7 % of that of the single-photon-based QSDC protocol.