⚛️ quantum physics

Technical Report OFDM-Assisted Simultaneous Quantum and Classical THz Communications

This paper proposes and validates an OFDM-based Simultaneous Quantum and Classical Communication (SQCC) system for frequency-selective Terahertz channels, demonstrating that it achieves practical secret key rates across a wide range of power sharing scenarios, significantly outperforming existing single-carrier schemes that require the classical signal to be over 100 times stronger than the quantum signal.

Original authors: Xin Liu, Chao Xu, Soon Xin Ng, Mohammed El-Hajjar, Phuc V. Trinh, Shinya Sugiura, Lajos Hanzo

Published 2026-09-18

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CC BY 4.0

Original authors: Xin Liu, Chao Xu, Soon Xin Ng, Mohammed El-Hajjar, Phuc V. Trinh, Shinya Sugiura, Lajos Hanzo

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 authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the race to build the next generation of secure communication networks, scientists are looking toward two distinct frontiers that have traditionally operated in separate lanes. On one side lies quantum communication, a method of sending information that relies on the fundamental laws of physics to guarantee secrecy. Unlike traditional encryption, which can be broken by powerful computers, quantum keys are theoretically unbreakable because any attempt to spy on them inevitably alters the signal, revealing the intruder. On the other side is the terahertz band, a slice of the electromagnetic spectrum sitting between microwaves and light. This band promises to carry vast amounts of data at incredible speeds, essential for future wireless networks, but it is notoriously difficult to use because the signals weaken rapidly and bounce unpredictably off walls and objects. For years, researchers have treated these two technologies as separate challenges, often requiring different hardware and transmission methods. The question that has remained unanswered is whether these two very different types of signals can travel together on the same path without destroying each other, especially in the messy, real-world environment where signals bounce and scatter.

A team of researchers has tackled this problem by proposing a new way to send both a secret quantum key and a standard data stream simultaneously over terahertz waves. Their work focuses on a specific hurdle: the fact that in a real building or outdoor space, terahertz signals do not travel in a straight line. Instead, they hit surfaces and scatter, creating multiple versions of the same signal that arrive at the receiver at slightly different times. This phenomenon, known as frequency-selective fading, scrambles the information and makes it extremely difficult to decode. Previous attempts to combine quantum and classical signals in this band assumed a perfectly clear path, a condition that rarely exists outside of a controlled laboratory. The researchers realized that to make this technology practical, they needed a system that could untangle these scattered signals while keeping the delicate quantum information safe from the much stronger classical data stream.

To solve this, the team designed a system that uses a technique called orthogonal frequency division multiplexing, or OFDM. Imagine a highway where traffic is usually forced into a single lane; if that lane gets blocked by a pothole or debris, the whole line stops. In contrast, the OFDM approach splits the data into many smaller, parallel lanes, or subcarriers. If one lane encounters a problem caused by a bouncing signal, the others can still get through, and the system can reconstruct the full message from the pieces that arrived intact. The researchers applied this concept to a hybrid system where a strong classical signal, carrying ordinary data, is superimposed with a very weak quantum signal, carrying the secret key. Because the quantum signal is so faint, the strong classical signal can easily drown it out or distort it. The challenge is to let the classical signal pass through clearly while stripping away its interference to reveal the hidden quantum message.

The researchers built a simulation to test how this system would perform in a realistic indoor environment with walls and obstacles. They compared their new OFDM-based approach against a simpler method that sends signals in a single stream, known as single-carrier transmission. In the simulations, the single-carrier method struggled significantly. It required the classical signal to be at least one hundred times stronger than the quantum signal just to maintain a basic level of security. If the power balance shifted even slightly, the system would fail to generate a secure key. The new OFDM system, however, proved far more resilient. It successfully maintained a secure connection across a much wider range of power settings, allowing the two signals to coexist without the classical data overwhelming the quantum key. This flexibility is crucial because it means the system can adapt to different distances and conditions without needing to drastically increase the power of the classical signal, which would otherwise disrupt the quantum transmission.

The study also examined how the system handles the inevitable errors that occur when signals bounce around a room. When the receiver tries to decode the strong classical signal first, it might make a small mistake. In a traditional setup, this error would corrupt the quantum signal, making it impossible to extract the secret key. The researchers developed a process where the receiver first decodes the classical data, then mathematically removes that data from the combined signal to leave behind the clean quantum information. They found that even if the classical decoding was not perfect, the system could still recover the quantum key, provided the error rate remained within a manageable limit. This was demonstrated in simulations where the system operated successfully over distances of up to several hundred meters, depending on the specific conditions of the room and the balance of power between the two signals.

One of the most significant findings was that the new system works well even when the environment is not ideal. In scenarios where the signal quality was poor, the OFDM approach still managed to generate a secure key, whereas the older single-carrier method failed completely. The researchers noted that the system's success relies on a careful balance; if the quantum signal is too weak relative to the classical one, it gets lost in the noise, but if it is too strong, it interferes with the classical data. Their simulations identified a sweet spot where both signals could be decoded reliably. This suggests that in a future network, devices could share the same terahertz antenna to send both high-speed internet data and unbreakable security keys, eliminating the need for separate hardware and reducing the cost and complexity of secure communication.

While the results are promising, the researchers are clear that these findings come from computer simulations rather than physical experiments in the real world. They have mapped out the theoretical limits and shown that the concept is sound, but they acknowledge that building a physical device involves additional challenges, such as the precision of the electronic components and the stability of the signal in a moving environment. The work serves as a blueprint, proving that the physics allows for this dual transmission in a way that was previously thought too difficult. By showing that frequency-selective fading can be managed rather than avoided, the study opens a path toward integrating quantum security directly into the high-speed wireless networks of the future, ensuring that the data of tomorrow is protected by the laws of physics today.

Problem Statement

The paper addresses the challenge of implementing Simultaneous Quantum and Classical Communication (SQCC) in Terahertz (THz) bands over frequency-selective multipath fading channels. While existing THz SQCC research has primarily focused on optical fiber or assumed flat-fading channels, real-world wireless THz environments suffer from severe path loss and frequency-selective dispersion due to multipath effects. Furthermore, current SQCC architectures often rely on single-carrier (SC) transmission, which struggles with inter-symbol interference (ISI) in dispersive channels. A critical unresolved issue is the power sharing between the strong classical signal and the weak quantum signal; in SC-based THz SQCC, the classical signal must be significantly stronger (at least 100 times) to avoid overwhelming the quantum channel, limiting the flexibility and efficiency of the system. Additionally, the mutual interference between the demodulation of the classical signal and the extraction of the quantum key in frequency-selective environments has not been fully investigated.

Methodology

The authors propose and analyze an OFDM-based SQCC system designed for time-invariant, frequency-selective THz fading channels, contrasting it with a Single-Carrier (SC) baseline.

System Architecture:
- Signal Superposition: Both the classical communication signal (using BPSK or QPSK) and the Continuous Variable Quantum Key Distribution (CV-QKD) signal (using Gaussian Modulation of Coherent States, GMCS) are superimposed onto the same physical waveform.
- Modulation Domain:
  - In the SC scheme, signals are superimposed in the Time Domain (TD).
  - In the OFDM scheme, signals are superimposed in the Frequency Domain (FD) across multiple subcarriers, transforming the frequency-selective channel into parallel flat-fading sub-channels.
- MIMO and Beamforming: Both systems utilize Multiple-Input Multiple-Output (MIMO) configurations with analog beamforming to mitigate severe THz path loss. The beamformers are tuned to the Line-of-Sight (LoS) component.
- Reception and Interference Cancellation: The receiver (Bob) employs a Successive Interference Cancellation (SIC) approach:
  1. Demodulate the strong classical signal first.
  2. Reconstruct the classical displacement based on the detected bits.
  3. Subtract the reconstructed classical signal from the composite received signal to isolate the quantum signal.
  4. Perform CV-QKD post-processing (sifting, reconciliation, privacy amplification) on the residual quantum signal.
Reconciliation and Security Analysis:
- The paper models the impact of imperfect classical demodulation as a residual displacement in the quantum signal. An erroneous classical bit decision introduces a discrete error term ( $r_{SIC}$ ) that degrades the Signal-to-Noise Ratio (SNR) for reconciliation.
- LDPC Coding: Low-Density Parity-Check (LDPC) codes are used for multidimensional reconciliation to correct errors in the quantum data.
- Secret Key Rate (SKR): The SKR is calculated using the finite-size security framework, accounting for the Block Error Rate (BLER) of the reconciliation step, the reconciliation efficiency ( $\beta$ ), and the Holevo information bound under collective attacks. The analysis explicitly links the classical Bit Error Rate (BER) to the quantum reconciliation performance.

Key Contributions

The paper claims the following novel contributions:

First Investigation of Frequency-Selective THz SQCC: Unlike prior works limited to flat fading or optical fiber, this work constructs an SQCC model specifically for frequency-selective multipath THz channels.
OFDM-Based SQCC Proposal: The authors propose an OFDM-based multi-carrier SQCC system where classical and quantum signals are superimposed in the frequency domain to mitigate multipath effects, contrasting with the time-domain superposition of SC systems.
Integrated Beamforming: The study intrinsically combines beamforming with both SC and OFDM SQCC systems to address THz path loss, analyzing how beamforming gain impacts the equivalent quantum channel.
Power Sharing and Interference Analysis: The work investigates the trade-off between classical and quantum power sharing ( $\zeta = P_Q/P_C$ ). It demonstrates that imperfect demodulation of the classical signal contaminates the quantum channel, and vice versa, requiring careful power allocation.
Performance Comparison: The study provides a comprehensive comparison showing that the OFDM-based scheme achieves practical SKR over a wide range of power sharing ratios, whereas the SC-based scheme requires the classical signal to be at least 100 times stronger than the quantum signal to function effectively in THz SQCC.

Results

Simulations were conducted using 4x4 MIMO dimensions, a carrier frequency of 15 THz, and LDPC reconciliation (rate 0.5). Key findings include:

BER Performance: The OFDM-based system consistently outperforms the SC-based system in terms of Bit Error Rate (BER) for classical communication across all power sharing ratios ( $\zeta$ ). For instance, at $\zeta=0.01$ , the OFDM system achieves a BER of $10^{-5}$ at 10 dB SNR, while the SC system exhibits an error floor.
Reconciliation BLER: In frequency-selective fading, the SC-based system requires a very low $\zeta$ (0.01) to achieve an acceptable Block Error Rate (BLER $\le 0.1$ ) for SKR generation. In contrast, the OFDM-based system maintains acceptable BLER performance across a broader range of $\zeta$ (including 0.05 and 0.1), particularly in channels with a higher Ricean factor ( $K=10$ dB).
Secret Key Rate (SKR) and Distance:
- The OFDM-based system achieves a positive SKR over significantly longer distances than the SC system.
- At $K=0$ dB, the SC system achieves a secure distance of only 12 meters at $\zeta=0.01$ . The OFDM system, however, supports reliable reconciliation and positive SKR at much greater distances and higher power sharing ratios (e.g., $\zeta=0.1$ ), resulting in higher reconciliation efficiency ( $\beta$ ).
- Increasing the Ricean factor ( $K=10$ dB) improves performance for both systems, but the SC system still struggles to support higher $\zeta$ values compared to the OFDM system.

Significance and Claims

The paper asserts that its primary significance lies in demonstrating that OFDM is a necessary enabler for practical SQCC in realistic, frequency-selective THz channels.

Overcoming SC Limitations: The authors claim that the SC-based approach is fundamentally limited in THz SQCC because the severe multipath dispersion forces the classical signal to dominate the power budget (by a factor of 100) to ensure reliable demodulation, which in turn starves the quantum signal of power.
Broadening Operational Range: By resolving the frequency-selective channel into parallel subcarriers, the OFDM-based receiver improves classical detection integrity. This allows for a wider range of power sharing ratios between classical and quantum signals, leading to higher reconciliation efficiency and longer secure transmission distances.
Distinction from Prior Work: The paper distinguishes itself from previous THz SQCC studies (which focused on flat fading or optical fiber) and pure CV-QKD studies by addressing the specific coupling of classical demodulation errors and quantum reconciliation in a dispersive wireless environment.

The authors conclude that while their work focuses on stationary, frequency-selective scenarios, it lays the groundwork for future investigations into doubly selective channels (using OTFS), beam-squint effects, and practical receiver impairments.

Problem Statement

Methodology

Key Contributions

Results

Significance and Claims

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