Quantum Key Distribution Using Optimum Expectation Values of Maximally Entangled GHZ States

We propose a new quantum key distribution scheme that is based on the optimum expectation values of maximally entangled Greenberger-Horne-Zeilinger states. Our protocol makes use of the degrees of freedom in continuously variable angles, thereby increasing the security of the key distribution. Outlined are two protocols that distribute a key from Alice to Bob using the above idea, followed by an extension that allows for the same key to be shared with Charlie. We show how this scheme provides for certain detection of any eavesdropper through absolute violation rather than the probabilistic violation used in many protocols.