Reference-frame-independent Quantum secure direct communication

TL;DR

The paper tackles reference-frame misalignment in quantum secure direct communication (QSDC) for mobile channels by introducing a reference-frame-independent QSDC (RFI-QSDC) that requires calibrating only one frame direction and tolerates a misalignment angle $β$ in the other directions. It develops a β-independent invariant $C$ to bound Eve's information, derives a closed-form secrecy capacity bound $C_s$ in terms of measurement invariants, and provides a security proof against collective and photon-number-splitting attacks. A system model with a decoy-state method and intensity optimization is constructed to evaluate performance under channel attenuation, showing substantially extended distances compared to single-photon QSDC; for example at $10$ dB attenuation the capacities are $8.765 \times 10^{-6}$ and $4.150 \times 10^{-6}$ bit/pulse for $β=0^{\circ}$ and $β=45^{\circ}$, with maximum distances of $27.875$ km and $26.750$ km. Overall, the work offers a viable pathway to deploy QSDC in dynamic mobile environments by stabilizing security against reference-frame fluctuations and optimizing operational parameters. $C_s = Q^{BAB}[1-h(E^{BAB})] - \left[ Q_{n=1}^{BAE} h\left( \frac{1+\sqrt{C/2}}{2} \right) + Q_{n\ge 2}^{BAE} \cdot 1 \right]$, where $C$ is the β-independent invariant and $Q$ denotes correlation-based gains.

Abstract

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 $β$ in the other two directions. To improve the protocol's robustness against reference frame fluctuations, we introduce a $β$-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 $8.765 \times10^{-6}$ bit/pulse and $4.150 \times10^{-6}$ 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.

Figures (2)

• Figure 1: The relationship between channel attenuation and secrecy message capacity of the protocol under different pulse intensities of the light source's signal state. The solid (dashed) lines in yellow, blue, and green correspond to the scenarios where the signal state intensities are 0.1, 0.05, and 0.01 with $\beta$=$0^{ \circ}$ ($45^{ \circ}$), respectively.
• Figure 2: Comparison of secrecy message capacity at the optimized intensity between RFI QSDC and single-photon-based QSDC Protocols. The red and green curves correspond to the RFI QSDC protocol with reference frame misalignment of $0^{ \circ}$ and $45^{ \circ}$, respectively, while the blue curve represents the single-photon-based QSDC protocol.