A Theoretical Scheme for Multi-user Quantum Key Distribution with N Einstein-Podolsky-Rosen Pairs on a Passive Optical Network

We propose a theoretical scheme for any-to-any multi-user quantum key distribution on a passive optical network with ordered N Einstein-Podolsky-Rosen pairs. This scheme is safe and more efficient than those with single photons. Its efficiency approaches 100% in the limit that the number of pairs used in eavesdropping check becomes negligible. It also has high capacity and is convenient for users.