⚛️ quantum physics

Long-distance quantum secure direct communication with Gottesman-Kitaev-Preskill qubits

This paper proposes a long-distance Quantum Secure Direct Communication (QSDC) protocol utilizing Gottesman-Kitaev-Preskill (GKP) qubits and third-generation quantum repeaters, demonstrating via numerical simulation that secure transmission over 1,000 km is achievable with 23 dB squeezing while introducing a cost-based optimization framework to balance distance, capacity, and resource deployment.

Original author: Meng-Dong Zhu, Jia-Wei Ying, Qi Zhang, Shi-Pu Gu, Xing-Fu Wang, Lan Zhou, Yu-Bo Sheng

Published 2026-11-10

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CC BY 4.0

Original author: Meng-Dong Zhu, Jia-Wei Ying, Qi Zhang, Shi-Pu Gu, Xing-Fu Wang, Lan Zhou, Yu-Bo Sheng

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the author. For technical accuracy, refer to the original paper. Read full disclaimer

In the invisible world of quantum physics, information is carried not by electric currents or radio waves, but by the delicate states of particles like light. These particles are incredibly fragile; as they travel, even the slightest interaction with their environment can scramble the data they hold, much like a whisper lost in a hurricane. For decades, scientists have sought a way to send these fragile messages over long distances without them dissolving into noise. A major breakthrough in this field involves a special way of encoding information called the Gottesman-Kitaev-Preskill, or GKP, code. Instead of trying to keep a single, perfect particle intact, this method spreads the information across a continuous wave of light, creating a pattern that is robust enough to survive small bumps and jolts. If the wave gets slightly distorted by noise, the pattern can be measured and corrected, allowing the original message to be recovered. This capability is essential for building a future where quantum computers and secure communication networks can operate over vast distances, connecting cities and continents without losing the precious data they carry.

Building on this foundation, a team of researchers has proposed a new method for sending secret messages directly, without needing to first share a password or key. This approach, known as quantum secure direct communication, allows two people to transmit a confidential message immediately. What makes this new proposal particularly significant is its ability to protect not just the data, but the people sending it. In modern conflicts, the location of a communication hub can be a target; if an enemy detects a signal, they can strike the source. This protocol offers a way to detect an eavesdropper in real-time. If the system senses that someone is listening, the communication stops instantly, and the personnel can move to a new location before their position is compromised. The researchers combined this direct communication method with a sophisticated network of "repeaters"—stations placed along the path that clean up the signal as it travels. By using the GKP code to fix errors at each stop, they showed that secure messages could theoretically travel over 1,000 kilometers, a distance previously thought to be nearly impossible for this type of direct transmission.

The core of the researchers' work lies in how they handle the inevitable loss of signal as light travels through fiber optic cables. In a standard setup, the signal fades away exponentially, becoming too weak to read after a certain point. To overcome this, the team designed a system where the message passes through a chain of intermediate stations. At each station, the light is not just amplified; it is actively corrected. The system uses a special type of error correction that works by comparing the message against a known reference pattern. If the pattern is slightly shifted by noise, the system measures the shift and pushes the signal back to its correct position. This process happens continuously as the message hops from one repeater to the next, effectively resetting the noise level before it can accumulate enough to destroy the information. The researchers simulated this process using a specific level of "squeezing," a technique that reduces the uncertainty in the light's properties, and found that with a squeezing level of 23 decibels, the system could maintain security over distances exceeding 1,000 kilometers.

However, simply adding more repeaters is not a perfect solution, as each station requires resources and time to operate. The researchers developed a framework to find the sweet spot between the distance covered, the amount of secret information that can be sent, and the cost of the equipment needed. They discovered that for a given distance, there is an optimal number of repeaters that minimizes the cost while maximizing the security. For example, to send a message over a certain distance, the most efficient setup uses just one repeater, achieving a high rate of secure information transfer. As the distance increases, the system requires more repeaters placed closer together to maintain the signal's integrity. The simulations showed that with 2,750 repeater nodes, the system could securely transmit data over 1,010 kilometers. This represents a massive leap forward, offering a communication range that is more than 200 times greater than what is possible without these repeaters.

The study also carefully considered the practical hurdles of building such a system. While the math and simulations are promising, the physical realization requires technology that is still maturing. The researchers noted that creating the high-quality light states needed for this process is currently difficult, and the equipment required to store and correct the light while it waits at each repeater station is complex. They explored two main paths for building this network: one using microwave-based storage systems that would need to be converted to optical signals, and another using purely optical methods that avoid the need for storage altogether. Both paths face challenges, particularly in generating the precise light patterns needed and synchronizing the equipment perfectly. Despite these engineering challenges, the theoretical work provides a clear roadmap. It demonstrates that by combining advanced error correction with a network of repeaters, it is possible to create a quantum communication network that is both secure and capable of spanning continents, offering a new layer of protection for sensitive communications in an increasingly connected world.

Technical Summary: Long-distance Quantum Secure Direct Communication with Gottesman-Kitaev-Preskill Qubits

Problem Statement
Quantum Secure Direct Communication (QSDC) enables the direct transmission of secret messages without prior key distribution and offers the unique capability to detect eavesdropping in real-time, thereby protecting the physical safety of communication personnel by allowing immediate relocation upon detection of an attack. However, long-distance QSDC faces significant hurdles. First-generation quantum repeaters, which rely on entanglement purification, are unsuitable for QSDC because the purification process erases the encoded information. While Quantum Error Correction (QEC) codes offer a potential solution, implementing them over long distances requires overcoming exponential photon loss and accumulated noise. Existing protocols are largely limited to point-to-point communication or short distances due to channel attenuation and the lack of scalable error correction architectures compatible with direct message transmission.

Methodology
The authors propose a long-distance QSDC protocol utilizing Gottesman-Kitaev-Preskill (GKP) qubits integrated with third-generation quantum repeaters. The methodology relies on the following core components:

GKP Encoding: The protocol encodes quantum information into the infinite-dimensional Hilbert space of a harmonic oscillator using GKP states. These states possess a lattice periodic structure in phase space, enabling the correction of small displacement errors induced by noise. The protocol utilizes finite-squeezed GKP states, modeled as Gaussian peaks within a larger envelope, to approximate ideal logical states ( $|0_L\rangle, |1_L\rangle, |+L\rangle, |-L\rangle$ ).
Third-Generation Repeater Architecture: Unlike first-generation repeaters, this architecture does not use entanglement purification. Instead, it employs a chain of repeater nodes where each node performs continuous-variable (CV) error correction. The process involves:
1. Error Correction: Using Steane error-correction structures with ancillary GKP states ( $|0_L\rangle$ and $|+L\rangle$ ) and controlled-X (SUM) gates to measure syndromes and correct displacement errors in the $\hat{q}$ and $\hat{p}$ quadratures.
2. Optical Amplification: Applying amplification operations to partially compensate for channel loss before the state is transmitted to the next node.
3. Variance Reset: The error correction and amplification process resets the effective displacement-noise variance to a manageable level ( $c_{opt}\sigma^2_{GKP}$ ) at each node, preventing the exponential accumulation of errors.
Protocol Steps:
1. Forward Transmission: Bob prepares a sequence of GKP states and transmits them to Alice through a chain of $N_{QR}$ repeater nodes.
2. Security Check (Alice): Alice performs random sampling for eavesdropping detection by measuring syndromes on selected states. If the Detection Bit Error Rate (DBER) is below a threshold (5.6%), she proceeds.
3. Encoding: Alice encodes secret bits (0 or 1) onto the remaining states using displacement operators ( $\hat{D}(0)$ or $\hat{D}((\sqrt{\pi} + i\sqrt{\pi})/\sqrt{2})$ ) and returns the states to Bob via the repeater chain.
4. Final Decoding: Bob performs error correction and homodyne detection. If the Quantum Bit Error Rate (QBER) is below the threshold (10.7%), he decodes the message.

Key Contributions

Protocol Design: The paper introduces the first QSDC protocol specifically designed for long-distance transmission using GKP qubits and third-generation repeaters, bypassing the limitations of entanglement purification.
Security Analysis: A rigorous security analysis is provided based on Wyner's wiretap channel theory, deriving the secrecy capacity ( $C_s$ ) under collective attacks. The analysis accounts for the continuous nature of syndrome measurements and the specific error rates of GKP states.
Cost-Based Optimization Framework: The authors establish a quantitative cost function $C(L_{all}, N_{QR})$ that balances the secrecy message capacity against the resource cost (repeater nodes and time steps). This framework allows for the optimization of repeater deployment for specific transmission distances.

Results
Numerical simulations were conducted assuming a fiber attenuation length of 22 km, coupling/detection efficiency of 0.98, and an initial squeezing level of 23 dB ( $\sigma_{GKP} \approx 0.05$ ).

Transmission Distance: The protocol demonstrates that secure transmission distances exceeding 1000 km are achievable. Specifically, with 2750 repeater nodes, a maximum distance of 1010.37 km is reached. This represents a ~215-fold increase over the repeater-free configuration (which is limited to 4.70 km).
Performance Scaling: Increasing the number of repeater nodes significantly extends the achievable distance. For instance, 120 nodes extend the range to 103.45 km, surpassing previous 100-km QSDC benchmarks.
Squeezing Sensitivity: The simulations indicate that while higher squeezing levels improve performance, the benefits diminish beyond a certain point. A 23 dB squeezing level is identified as a practical balance between performance and experimental feasibility.
Optimization: The cost-function analysis reveals that for a 3.46 km transmission, a single repeater node yields a minimum cost with a secrecy capacity of 0.70 bit/state. For longer distances, the optimal configuration involves denser repeater spacing, maintaining a secrecy capacity of approximately 0.67 bit/state over a broad range before resource constraints cause exponential decay.

Significance
The paper claims that this work demonstrates the potential of combining GKP error correction with third-generation quantum repeaters to facilitate long-distance QSDC and scalable quantum networks. By enabling direct message transmission with built-in error correction, the protocol addresses the critical need for secure communication over global distances. Furthermore, the ability to detect eavesdropping in real-time offers a unique tactical advantage in protecting communication personnel from physical threats (e.g., "decapitation strikes" in modern warfare) by allowing immediate relocation before information leakage occurs. The proposed cost-based optimization framework provides a systematic design strategy for deploying scalable quantum repeater architectures, bridging the gap between theoretical error correction and practical, long-distance quantum communication infrastructure.

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