While all cloud based platforms possess security vulnerabilities, the additional security challenges with container systems stem from the sharing of Host OS among independent containers. If a malicious application was to break into the root of container Daemon, it could gain root access into the host kernel thereby compromising the entire system. It could create Denial-Of-Service attack for other user applications, rejecting service to other applications. In this paper, we propose a quantum network security framework for the cloud. We devise a means by which quantum particles, denoted entangled bell pairs, are routed to network nodes. This enables teleportation of quantum information between source and destination only when root privileges are required by an application. The secure quantum channel works on a use-once only policy, so the key data cannot be easily copied, regenerated or spoofed without detection. A network framework for multiple pre-staged channels is devised and we illustrate that policy for network routing of entangle particles formulated as a multi-tenant teleportation network, capable of disseminating key data to servers hosting Docker container applications. The framework can achieve provably high levels of security and is capable of integration into a cloud data center for securing applications using Docker Containers. We also describe quantum network layer protocols for cloud container security that leverage the unique properties of quantum entanglement. To resolve security concerns, this layer would control access between application and container daemon, thereby facilitating restricted communication with proper authentication.