Multi-user quantum key distribution with collective eavesdropping detection over collective-noise channels
Huang Wei†a),b), Wen Qiao-Yana), Liu Bina), Gao Feia)
       
Definition of the function r ( U ) = r , where λ 1, λ 2, λ 3, and λ 4 are eigenvalues of the matrix U , and r is the distance between the origin of the complex plane o and the polygon λ 1 λ 2 λ 3 λ 4. Obviously, r = 0 indicates that o is in/on the polygon λ 1 λ 2 λ 3 λ 4.