High-Dimensional Quantum Key Distribution with <em>N</em>-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 dN and accordingly a very high security. We present the implementation of this protocol in different types of optical fibers where the mentioned states undergo perturbations under propagation in optical fibers; such perturbations can be notably reduced in a passive (autocompensation) or active way and importantly the N-qubits present a great robustness against such optical perturbations. Likewise, quantum states also undergo attenuation, that is, some photons are lost under propagation in the optical fibers and then effective N′ (&lt; N)-qudits are obtained which also are used to generate secret keys. In fact, the detection of states combines standard projective measurements along with photon coincidences. Besides, we analyze the security of this high-dimensional protocol under an intercept and resend attack realized by Eve, and the resulting secure key rates are calculated showing a significative increasing with the dimension provided by the number N of photons.