Single-Photon Transmission, Quantum Key Distribution, Multimode Fiber, and Higher-Order Poincaré Spheres

In this study, we simulate the propagation of a single photon propagating within a modal group, traversing a multimode optical fiber in the presence of mode coupling. We illustrate the propagation graphically on a group of higher-order Poincaré spheres. The spheres display the propagation of the light within the modal group, including polarization in time and in distance as the transmission proceeds. Thus, the amplitudes and the relative phases within the group can be visualized throughout the transmission, which is novel and very useful for understanding the propagation. At the fiber output, we show how to recover the input of a classical state using the simulated propagation information displayed on such multiple spheres. Once a classical modal path is established from end to end, one can transmit quantum states, for example, as a spatial–time binned QKD (quantum key distribution) code. A quantum state follows this classical path. Hence, it can include binary or qudit information. Accessing a photon output state is important for many quantum network applications, including quantum key distribution, routing, and entanglement swapping. In addition, one can use other modal groups within the same fiber to multiplex other quantum channels as well as multiplex within a modal group using principal modes, a more complicated communication method. This situation is also discussed while considering the use of the spheres. Their applications include higher-dimensional quantum communications, quantum cryptography, and quantum networks. It is important to point out that in today’s commercial quantum communications systems, quantum states are single-photon states, but they are not entangled. This includes both discrete and continuous variable quantum key distribution systems. Thus, in this report, we also address single-photon systems that are not entangled, unless stated otherwise.