## 1 Introduction  
As healthcare systems increasingly adopt the Internet of Medical Things (IoMT) [1, 2], ensuring secure communication becomes crucial. IoMT environments--comprising mobile and remote monitoring systems including wearable devices, implantable sensors, and telemedicine platforms--continuously collect and transmit highly sensitive patient data ranging from real-time vital signs to personal health records. This data sensitivity, combined with the distributed nature of IoMT networks, makes secure communication not merely important but absolutely crucial for maintaining patient privacy and regulatory compliance. Quantum key agreement (QKA) offers a compelling solution for secure communication in IoMT by allowing all participants to collaboratively generate a shared secret key using quantum principles. Unlike quantum key distribution (QKD), which relies on a trusted center to generate and distribute keys [3; 4; 5], QKA ensures that all parties contribute equally to the final key, enhancing fairness and reducing reliance on centralized infrastructure--features that are particularly desirable in distributed medical systems. Despite its potential, the application of QKA in practical settings such as IoMT remains underexplored, especially for protocols that avoid complex entanglement operations and authenticated classical channels. QKA addresses many of the limitations inherent in traditional QKD by allowing all parties to collaboratively establish a shared secret key, rather than relying on a single party to generate and distribute it. This collaborative approach proves particularly advantageous for IoMT environments, where medical devices, healthcare providers, and monitoring systems must operate as equal participants in a distributed network without hierarchical dependencies. As highlighted in [6], [PERSON] establishes that all \"one-sided two-party computations\"--where only one of the two parties learns the computation result--are inherently insecure. QKA, by design, avoids such asymmetry by requiring all involved parties to equally contribute to the key generation process. This equal contribution model aligns perfectly with IoMT's distributed medical systems, where wearable devices, remote sensors, and healthcare databases must maintain equivalent security privileges without relying on centralized key management infrastructure that could become a single point of failure in critical medical scenarios. This fundamental difference significantly reduces the risks associated with unilateral trust assumptions and central points of failure--characteristics that make QKA particularly desirable in distributed medical systems where patient safety and data integrity cannot depend on centralized authorities. However, despite QKA's compelling advantages for IoMT applications, its practical implementation in real-world medical environments remains significantly underexplored. This research gap is particularly pronounced for QKA protocols that avoid complex entanglement operations and authenticated classical channels--precisely the type of streamlined approaches most suitable for resource-constrained IoMT devices with limited computational capabilities and bandwidth constraints. The value of QKA lies in its inherent properties:  
* Fairness: No single participant holds complete control over the key generation process, ensuring mutual trust. * Network Compatibility: QKA protocols can often be implemented using less demanding hardware compared to QKD. * Enhanced Security: The distributed nature of QKA mitigates risks from insider threats and single-point vulnerabilities common in QKD-based systems. Since the pioneering work of [PERSON] et al. in 2004, who proposed the first QKA protocol using Einstein-Podolsky-Rosen (EPR) pairs [7], QKA has received increasing attention. In 2010, [PERSON] and [PERSON] [8] proposed a BB84-based [9] QKA scheme that incorporated delayed measurement and was proven effective against internal and external attacks.