Wireless body sensor network (WBSN) is an interdisciplinary field that could permit continuous health monitoring with constant clinical records updates through the Internet. WBAN is a special category of wireless networks. Coronavirus disease 2019 (COVID-19) pandemic creates the situation to monitor the patient remotely following the social distance. WBSN provides the way to effectively monitor the patient remotely with social distance. The data transmitted in WBSN are vulnerable to attacks and this is necessary to take security procedure like cryptographic protocol to protect the user data from attackers. Several physiological sensors are implanted in the human body that will collect various physiological updates to monitor the patient's healthcare data remotely. The sensed information will be transmitted wirelessly to doctors all over the world. But it has too many security threats like data loss, masquerade attacks, secret key distribution problems, unauthorized access, and data confidentiality loss. When any attackers are attacking the physiological sensor data, there is a possibility of losing the patient's information. The creation, cancellation, and clinical data adjustment will produce a mass effect on the healthcare monitoring system. Present-day cryptographic calculations are highly resistant to attacks, but the only weak point is the insecure movement of keys. In this paper, we look into critical security threats: secure key distribution. While sharing the secret key between communicating parties in the wireless body sensor networks in the conventional method like via phone or email, the attackers will catch the private key. They can decrypt and modify more sensitive medical data. It can cause a significant effect like death also. So need an effective, secure key distribution scheme for transmission of human body health related data to medical professional through wireless links. Moreover, a new enhanced BB84 Quantum cryptography protocol is proposed in this paper for sharing the secret key among communicating parties in a secure manner using quantum theory. Besides, a bitwise operator is combined with quantum concepts to secure the patient's sensed information in the wireless environment. Instead of mail and phone via sharing secret key, quantum theory with the bitwise operator is used here. Therefore, it is not possible to hack the secret key of communication. The body sensor's constrained assets as far as battery life, memory, and computational limit are considered for showing the efficiency of the proposed security framework. Based on experimental results, it is proven that the proposed algorithm EBB84QCP provides high secure key distribution method without direct sharing the secret key and it used the quantum mechanism and bitwise operator for generating and distributing secret key value to communicating parties for sensitive information sharing in the wireless body sensor networks.