High-speed phase-encoded quantum secure direct communication over 11.4 km heterogeneous free-space and fiber links

Robust quantum transmission is driving a new paradigm in space-ground quantum networking. Although phase encoding has been widely adopted in terrestrial fiber channels, it has long been considered unsuitable for free-space quantum communication. Here, we demonstrate phase-encoded quantum communication over 1400 m of urban free space. The system maintained stable operation for nearly one hour, achieving 99.07% interference visibility and an average quantum bit error rate of 2.38%. The free-space quantum states were directly coupled into the fiber and transmitted over an additional 10 km, confirming seamless interoperability across different media. We further show that turbulence-induced phase drifts between successive picosecond pulses can be effectively compensated. A cascaded-link model and numerical simulations indicate feasibility over free-space distances exceeding 30 km, underscoring the potential for satellite-to-ground quantum links. This work establishes the viability of phase encoding in free-space quantum networks, simplifying cross-medium integration and enabling compatibility with existing classical infrastructures.

💡 Research Summary

This paper presents the first experimental demonstration of high‑speed phase‑encoded quantum secure direct communication (QSDC) over a heterogeneous link that combines 1.4 km of urban free‑space propagation with a subsequent 10 km of standard single‑mode fiber, yielding a total distance of 11.4 km. The authors employ a 1.25 GHz weak‑coherent laser source emitting 50 ps pulses at 1549.32 nm. An intensity modulator creates signal, decoy, and vacuum states in a 30:2:1 ratio (μ = 0.71, ν₁ = 0.28, ν₂ = 0). Phase encoding is realized with a Faraday‑Sagnac‑Michelson interferometer followed by two cascaded phase modulators that together generate four possible phase values {0, π/2, π, 3π/2}. After the interferometer, each pulse is split into two temporally separated components (400 ps apart) and multiplexed in wavelength at a 500 kHz clock.

The free‑space segment is realized across a lake in Hefei, China, using a passive telescope with a 120 mm entrance pupil and 27.1× magnification. The received beam is coupled directly into a single‑mode fiber via a triplet fiber‑optic collimator, minimizing spatial mode disturbances. At the fiber end, a 10 km link transports the quantum states to the receiver, where a dual‑channel InGaAs/InP single‑photon detector (SPD) operating at 1.25 GHz provides 20 % detection efficiency, a dark count rate of 10⁻⁶ cps, and an after‑pulse probability of 1 %. The total loss at the receiver is 6.5 dB.

A key technical contribution is the real‑time phase‑drift compensation scheme. The system continuously monitors interference visibility, extracts the instantaneous phase error, converts it into a voltage offset, and feeds it back to the phase modulators. Because atmospheric turbulence varies on the order of 0.01–0.1 s, while the separation between successive pulses is only 400 ps, consecutive pulses experience essentially identical turbulence conditions. This temporal proximity allows the feedback loop to correct slow phase drifts effectively, preserving high visibility even under moderate turbulence.

Two experimental sessions were conducted under different atmospheric conditions (wind level 2, visibility 24 km, 60 % humidity; and wind level 1, visibility 14 km, 40 % humidity). Over nearly one hour of continuous operation, the system achieved an average interference visibility of 99.07 % and a quantum bit error rate (QBER) of 2.38 %. The first session suffered a brief link interruption due to beam misalignment; the built‑in acquisition‑pointing‑tracking (APT) system restored operation after recalibration. The second session ran uninterrupted, demonstrating the robustness of the phase‑compensation mechanism.

The communication protocol employed is the simultaneous transmission of information and key exchange (STIKE), a one‑way quasi‑QSDC scheme that integrates quantum direct communication with quantum key distribution (QKD). In each frame (125 bytes) a spreading factor of 1:1920 is applied to tolerate loss fluctuations. Measured secure communication rates were 4.22 kbps (first day 3.90 kbps). Key generation rates were 13.51 kbps and 30.42 kbps, while key consumption rates were 21.18 kbps and 27.68 kbps, respectively. The key‑recycling efficiency reached 99.9 %–99.97 %, matching the theoretical prediction 1 − Qμ/2.

Numerical simulations extending the free‑space segment to >30 km, assuming an 80 % detector efficiency, a 1 m receiving telescope, and a conversion efficiency of 10⁻¹⁵, indicate that QBER remains below 5 % and key generation can exceed consumption, confirming feasibility for satellite‑to‑ground links. The authors argue that the combination of real‑time phase feedback, spatial mode filtering via fiber coupling, and the STIKE protocol’s adaptive allocation of random numbers versus key material provides a scalable, resource‑efficient architecture for future quantum networks.

In conclusion, the work overturns the long‑standing belief that phase encoding is unsuitable for free‑space quantum channels. By exploiting the short temporal separation of pulses and implementing active phase stabilization, the authors achieve performance comparable to state‑of‑the‑art fiber‑based systems while maintaining seamless interoperability between free‑space and fiber media. This advances the practical deployment of heterogeneous quantum networks, particularly for satellite‑ground scenarios where a unified encoding scheme can dramatically reduce system complexity, cost, and the need for multiple specialized transceivers. Future directions include integration of adaptive optics, larger aperture telescopes, higher‑efficiency detectors, and multi‑channel parallelization to push both distance and data rate toward the limits required for a global quantum internet.