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

Daniel A. Nolan

Published Apr 2, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.20944/preprints202512.1540.v3

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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. 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.
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.
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.
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.
Higher dimensional communications in optical fiber enables new possibilities including increased transmission capacity and hyperentangled state transfer. Mode coupling among channels during transmission however causes interference among channels and limits detection. In classical optical communications, MIMO (modes in modes out) is a means to deal with this issue, however it is not possible to utilize this technology in quantum communications due to power limitations. Principal mode transmission is a another means to deal with mode coupling and signal interference among channels. Conceptually, this can be used in quantum communications with some limitations. In this report, we numerically simulate this process using the time delay method and show how it can be implemented using 2 and 4 higher dimensional quantum states, such as W or GHZ states. These numerical simulations are very illustrative of how the implementation proceeds.
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.
Quantum communication, i.e., the ability to transport a quantum state from one place to another, represents a crucial task for many quantum applications, i.e. quantum cryptography, quantum secret sharing and quantum networks. However current systems present main limitations in terms of low information rates, short propagation distances and low compatibility with today classical optical infrastructure. These restrictions bound the development of this field and its practical applications. High-dimensional quantum communication can help in overcoming these challenges enhancing the information rate and the system error tolerance. We here report our recent results on high-dimensional fiber based quantum communication, both with multicore and multimode fibers, in which we prove the capability of preparing, manipulating, transmitting and measuring advanced quantum states with excellent fidelities. Our results pave the way towards high-dimensional quantum communication in an optical fiber infrastructure.