# Estimating Interception Density in the BB84 Protocol: A Study with a Noisy Quantum Simulator
###### Abstract  
Quantum computers have the potential to break the public-key cryptosystems widely used in key exchange and digital signature applications. To address this issue, quantum key distribution (QKD) offers a robust countermeasure against quantum computer attacks. Among various QKD schemes, BB84 is the most widely used and studied. However, BB84 implementations are inherently imperfect, resulting in quantum bit error rates (QBERs) even in the absence of eavesdroppers. Distinguishing between QBERs caused by eavesdropping and QBERs due to channel imperfections is fundamentally infeasible. In this context, this paper proposes and examines a practical method for detecting eavesdropping via partial intercept-and-resend attacks in the BB84 protocol. A key feature of the proposed method is its consideration of quantum system noise. The efficacy of this method is assessed by employing the Quantum Solver library in conjunction with backend simulators inspired by real quantum machines that model quantum system noise. The simulation outcomes demonstrate the method's capacity to accurately estimate the eavesdropper's interception density in the presence of system noise. Moreover, the results indicate that the estimation accuracy of the eavesdropper's interception density in the presence of system noise is dependent on both the actual interception density value and the key length. BB94; quantum key distribution (QKD); partial intercept-and-resend; interception density; quantum bit error rates (QBER) +
Footnote †: journal: _Future Internet_  
of QKD services into its network, as well as the necessary hardware and software solutions for maintaining and monitoring a QKD-secured network. The growing interest in practical applications of QKD protocols in recent years is also evidenced by the establishment of the European Quantum Communication Infrastructure (EuroQCI) project [6]. This infrastructure will consist of a terrestrial fiber-optic segment and a satellite network connecting strategic sites nationally and across borders to safeguard the privacy of sensitive and critical data for governmental institutions, their data centers, hospitals, and more. In the context of smart grid infrastructure security, the work [7] utilizes QKD secret keys over the MQTT protocol to support distributed energy resource (DER) communication. The practical implementation was tested in a real utility environment at the Electric Power Board (EPB) in Chattanooga, Tennessee, between a data center and an electrical substation connected via optical fiber. In another recent work [8], the application of QKD is discussed for communication channels in hydropower facilities. This implementation encrypts and decrypts command/control communications, mitigating security risks while integrating with existing control interfaces. Moreover, Ref. [9] demonstrates the implementation of quantum-safe 100 Gbps IPsec VPN tunnels over 46 km of fiber between two data centers, achieving a secret key rate of 7.4 kbps. Another promising application is presented in [10], which showcases and tests a real-time implementation of a submarine QKD system based on the BB84 protocol using an FPGA as a photon counting module. QKD enables the secure sharing of a secret key between two parties, traditionally referred to as [PERSON] and [PERSON], over a quantum channel. An eavesdropper, [PERSON], may attempt to intercept the communication during this process. Several QKD protocols have been proposed, with the Brassard-Bennett 1984 (BB84) protocol being the first and most widely adopted [11]. Due to its prominence and practical applications, this study focuses on the four-state BB84 protocol as the foundational model for QKD. The robustness of the protocol and its widespread use make BB84 an ideal candidate for investigating the effectiveness and security of QKD in real-world scenarios. This paper advocates for a deeper investigation into the detectability of eavesdroppers, a non-trivial and unique feature of QKD.