High-Dimensional Quantum Key Distribution with N-Qudits States in Optical Fibers

We present a high-dimensional quantum key distribution protocol by using N-qudits quantum light states—that is, product states with N photons, each of them in a quantum superposition of dimension d, which provides a high dimension $d^N$ and, accordingly, a very high security level. We present the implementation of this protocol in different types of optical fibers, where quantum states can undergo polarization and phase perturbations under propagation in optical fibers; however, polarization perturbations can be notably reduced in a passive or active way, and, more importantly, these states can become insensitive to phase perturbations. Thus, N-qubits are fully robust to relative phase perturbations between any pair of 1-qubits, and therefore do not require any phase compensation, which, on the contrary, is absolutely necessary in high-dimensional QKD with 1-qudits (one photon). Likewise, quantum states also undergo attenuation, that is, some photons are lost under propagation in the optical fibers and thus $N^{\prime }(<N)$-qudits are used; however, even for standard optical fiber attenuation values, high secret key rates are still obtained. Finally, we analyse the security of this high-dimensional protocol under an intercept and resend attack performed by Eve, and the resulting secure key rates are calculated, showing a significant increase with the dimension provided by number N of photons.