Qudit Propagation Through Multimode Optical Fiber and the Geometry of the Quantum State

We simulate the propagation of a W states through an optical fiber in the presence of mode coupling. We illustrate the propagating quantum state graphically on a group of higher order Poincaré spheres. The spheres show the propagation of the light in time and in distance as the transmission proceeds. Thus, the amplitudes and the relative phases of the modal propagation can be visualized throughout the transmission, which is novel and very useful to understand the propagation. At the fiber output we show how to recover the input quantum state using the simulated quantum state information displayed on the multiple spheres. The geometry of these states is an SU(N) quantum geometry. Applications include higher dimensional quantum communications, quantum cryptography, and quantum networks, and longer-term quantum optical computing.