⚡ electrical engineering

Secret Key Rate Analysis of RIS-Assisted THz MIMO CV-QKD Systems under Localized and Global Eavesdropping

This paper analyzes the secret key rate of RIS-assisted THz MIMO continuous-variable quantum key distribution systems under localized and global eavesdropping scenarios, deriving novel rate expressions and developing a particle swarm optimization framework to maximize performance by optimizing RIS phase configurations.

Original authors: Sushil Kumar, Soumya P. Dash, George C. Alexandropoulos

Published 2026-03-31

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Sushil Kumar, Soumya P. Dash, George C. Alexandropoulos

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

Imagine you are trying to send a top-secret message to a friend across a vast, noisy desert. In the old days, you might have used a complex code (like RSA encryption) to hide your message. But with the rise of super-fast "quantum computers" on the horizon, those old codes are like writing a secret in invisible ink that a smart kid can easily wash away.

To solve this, scientists use Quantum Key Distribution (QKD). Think of this not as sending a message, but as sending a fragile, magical glass ball. If anyone tries to peek at the ball while it's flying, the glass cracks, and the sender and receiver know immediately that someone is listening.

This paper explores a high-tech way to make this magic glass ball travel much further and safer, specifically using Terahertz (THz) waves (a type of super-fast radio wave) and a new technology called RIS (Reconfigurable Intelligent Surface).

Here is the breakdown of their idea using simple analogies:

1. The Problem: The "Foggy Desert"

Sending these fragile quantum signals over long distances is hard.

The Signal: Imagine trying to shout a secret across a desert. The wind (atmosphere) and heat (noise) swallow your voice.
The Frequency: They are using Terahertz waves. These are like high-pitched whistles that carry a lot of data but get lost very quickly in the air, especially if there's no direct line of sight (like if a building is in the way).
The Thief (Eve): There is a spy named Eve. She wants to listen in. In the worst-case scenario, she has a "super-spy suit" that lets her listen to the entire path of the signal from start to finish.

2. The Solution: The "Magic Mirror Wall" (RIS)

To fix the signal loss, the authors introduce a Reconfigurable Intelligent Surface (RIS).

The Analogy: Imagine the desert is blocked by a wall. You can't shout over it. But, you have a giant wall made of thousands of tiny, smart mirrors (the RIS).
How it works: You can electronically tell each tiny mirror to tilt just the right amount. Instead of the signal hitting a wall and dying, the mirrors catch the signal, bounce it, and focus it like a laser beam straight to your friend.
The MIMO Part: Instead of one mirror, they use a whole array of antennas (MIMO) at both ends, like having a choir of singers instead of just one person, making the signal much stronger.

3. The Two Types of Spies (Eavesdropping Models)

The paper tests the system against two different types of spies to see how secure it really is:

Scenario A: The Localized Spy (The "Local Thief")
- The Analogy: Eve is a thief who can only hide in one specific spot. Maybe she is hiding near the sender, or near the mirror wall, or near the receiver, but she can't be everywhere at once.
- The Result: If she can only listen to one part of the journey, the system is very secure. The "glass ball" stays mostly intact because the thief only sees a tiny, blurry piece of the reflection.
Scenario B: The Global Spy (The "God-Mode Thief")
- The Analogy: This is the worst-case scenario. Eve has a "super-suit" that lets her listen to the entire journey at once, from the moment the ball leaves the sender until it hits the receiver. She sees the whole picture.
- The Result: This is much harder to defend against. However, even against this super-spy, the "Magic Mirror Wall" (RIS) helps significantly more than having no mirrors at all.

4. The "Smart Tuning" (Optimization)

Just having mirrors isn't enough; they need to be tilted perfectly.

The Analogy: Imagine a choir of 64 singers. If they all sing randomly, it's just noise. But if a conductor (an algorithm called Particle Swarm Optimization) tells every singer exactly when to sing and how loud, they create a perfect, powerful beam of sound.
The paper shows that using this "smart conductor" to tune the mirrors makes the secret key much faster and the communication range much longer.

5. The Big Takeaway

The researchers ran simulations (computer experiments) and found:

Mirrors Help: Adding the RIS (the mirror wall) dramatically extends how far you can send the secret key. Without it, the signal dies quickly. With it, you can go much further.
More Antennas = Better: Using more antennas (MIMO) makes the system stronger, like adding more lanes to a highway.
Local Spies are Easier to Beat: It is much easier to keep secrets safe if the spy can only listen to a small part of the path, rather than the whole thing.
Smart Tuning is Key: Randomly setting the mirrors is okay, but "smartly" tuning them (using the algorithm) makes the system perform at its absolute best.

Summary in One Sentence

This paper proves that by using a giant, smart "mirror wall" to bounce and focus fragile quantum signals, we can send ultra-secure keys over long distances in the future, even if a spy is trying to listen in, provided we tune the mirrors perfectly.

1. Problem Statement

The paper addresses the challenge of securing Terahertz (THz) wireless communications for next-generation (6G/B5G) networks. While THz frequencies offer high data rates, they suffer from severe path loss and are susceptible to eavesdropping. Traditional encryption (e.g., RSA) is vulnerable to quantum computing attacks. Quantum Key Distribution (QKD) offers a solution, but Continuous Variable QKD (CV-QKD) systems operating in the THz band face limitations in Secret Key Rate (SKR) and transmission distance due to channel degradation.

The specific problem tackled is the security analysis of a Multiple-Input Multiple-Output (MIMO) CV-QKD system assisted by a Reconfigurable Intelligent Surface (RIS). The authors aim to quantify the SKR under two distinct threat models:

Localized Eavesdropping: A realistic scenario where an eavesdropper (Eve) has physical access to only one segment of the communication link (Direct Alice-Bob, Alice-RIS, or RIS-Bob).
Global Eavesdropping: A worst-case benchmark where Eve has full control over the purification of the entire effective end-to-end channel.

2. Methodology

System Model

Architecture: A MIMO system with $N_T$ transmit antennas (Alice) and $N_R$ receive antennas (Bob), assisted by an RIS with $K$ passive reflecting elements.
Channel Modeling: The composite channel includes a direct Line-of-Sight (LoS) path and an RIS-reflected path. The channel is modeled as a passive linear Gaussian quantum channel.
Signal Propagation: Alice encodes secret keys using Gaussian-modulated coherent states. The signal propagates through a coherent superposition of direct and RIS-assisted paths. The system utilizes homodyne detection and Reverse Reconciliation (RR) at Bob's end, as RR is more robust for low transmittance values.
Quantum Modeling: The channel loss is modeled via unitary dilation, introducing environmental modes (vacuum noise) that interact with the signal.

Eavesdropping Models

Entangling-Cloner Attack: Eve is assumed to perform collective Gaussian attacks. She prepares Two-Mode Squeezed Vacuum (TMSV) states (EPR pairs), injecting one mode into the channel's environmental input and retaining the other (idler) in quantum memory.
Localized Scenarios: Eve accesses environmental modes associated with a specific segment ( $H_d$ , $H_t$ , or $H_r$ ). The remaining loss mechanisms are treated as trusted vacuum noise.
Global Scenario: Eve controls the purification of the total effective channel matrix $H$ , representing the most stringent security constraint.

Analytical Framework

SKR Derivation: The authors derived closed-form expressions for the achievable SKR. The SKR is calculated as the difference between the classical mutual information $I(A;B)$ $I (A; B)$ and the Holevo information $\chi(B;E)$ $χ (B; E)$ (the maximum information Eve can extract).
- $SKR = I(A;B) - \chi(B;E)$
Optimization: To maximize SKR, the paper formulates an optimization problem to determine the optimal RIS phase configuration matrix ( $\Phi$ ) and the beam splitter transmissivities ( $\eta_a, \eta_b$ ).
Algorithm: Due to the non-linear nature of the SKR with respect to RIS phases, a Particle Swarm Optimization (PSO) algorithm is employed to solve the optimization problem efficiently.

3. Key Contributions

Novel Framework: Proposed a comprehensive RIS-assisted THz MIMO CV-QKD framework that models the direct and reflected paths as a global passive Gaussian channel preserving canonical commutation relations.
Localized Eavesdropping Analysis: Introduced and analyzed realistic localized eavesdropping scenarios where Eve is restricted to specific propagation segments. This contrasts with previous works that often assumed global access.
Closed-Form Expressions: Derived analytical expressions for SKR under both localized and global eavesdropping models, accounting for homodyne detection and reverse reconciliation.
Optimization Strategy: Developed a PSO-based joint optimization framework for RIS phase shifts and beam splitter parameters to maximize the SKR.
Comparative Benchmarking: Provided a rigorous comparison between localized and global eavesdropping, demonstrating that physical constraints on Eve significantly improve system security.

4. Numerical Results and Discussion

The authors conducted extensive simulations using parameters typical for THz systems (e.g., 15 THz carrier frequency, atmospheric absorption loss).

Impact of Eavesdropping Model:
- Localized vs. Global: Systems under localized eavesdropping achieve significantly higher SKR compared to the global eavesdropping model. Restricting Eve to a single segment drastically reduces her information gain.
- Segment Sensitivity: When Eve controls the Alice-RIS ( $H_t$ ) link, the SKR is lower compared to when she controls the direct ( $H_d$ ) or RIS-Bob ( $H_r$ ) links. This is because compromising the first hop prevents the RIS from providing its full beamforming gain.
Impact of MIMO and RIS Size:
- Increasing the number of antennas ( $N_T, N_R$ ) and RIS elements ( $K$ ) significantly improves SKR and extends the secure transmission distance.
- Larger RIS arrays provide stronger passive beamforming gain, compensating for severe THz path loss, particularly in long-distance regimes.
Optimization Performance:
- The PSO-optimized RIS phase configuration consistently outperforms random phase configurations across all scenarios.
- The optimized system extends the secure communication range significantly compared to non-RIS systems.
Noise Sensitivity:
- As detector noise increases, the maximum secure distance decreases. However, larger MIMO configurations and optimized RIS settings provide greater robustness against noise.

5. Significance and Conclusion

This paper establishes RIS-assisted THz MIMO CV-QKD as a viable and promising solution for secure next-generation wireless networks.

Security Enhancement: It demonstrates that leveraging the physical constraints of wireless propagation (localized eavesdropping) combined with RIS technology can yield substantial security gains over worst-case global attack models.
Range Extension: The integration of RIS effectively mitigates the high path loss inherent in THz bands, enabling secure key distribution over longer distances than previously possible with direct links.
Practicality: The use of PSO for phase optimization offers a practical approach to configuring RIS elements in real-time to maximize security.

The work bridges the gap between quantum communication theory and practical 6G physical layer security, highlighting that intelligent surface manipulation is a critical enabler for secure, high-speed quantum networks. Future work suggested includes analyzing performance under imperfect Channel State Information (CSI) and hardware constraints like discrete phase quantization.