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Photonics

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

Daniel A. Nolan

Published Aug 31, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.3390/photonics13090832

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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.
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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. 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.
Higher dimensional communications are of interest for multiple reasons including increasing classical transmission capacity and more recently the quantum state transfer through these fibers using the many modes within the fibers. For quantum communications, this enables an increase in the number of bits per photon, increasing quantum fidelity, increasing error threshold and enabling hyperentanglement transfer among other possibilities. High dimensional quantum state transfer can be transported through multimode fiber using the many modes available. However, this transfer medium is limited by mode coupling among the various spatial and polarization modes. Here we consider how this mode coupling impacts the transfer process. We consider the fiber's modal properties including orbital angular momentum, modal group numbers, and principal modes. We also investigate and propose input and output optical components as well as fiber properties that mitigate the deleterious effects of mode coupling. We propose methods to circumvent this mode coupling using optical fibers, optical components and devices that are commercially available today or those that are undergoing intense global research such as Flat Optics.
Secure communication became extremely important in the Information Age. Quantum communication protocols have been developed to provide absolutely secure transmission of information. Historically, quantum key distribution (QKD) uses the two-dimensional polarization basis to encode information and the key element of long-distance communication is single-mode optical fiber. However, it intrinsically limits the information content to 1 bit per photon. Nowadays, significant effort is devoted to increase the data carrying capacity of a single quantum secure optical line. Large-core multimode fibers support a multitude of transverse optical modes and can potentially transfer information at much higher density.
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