We demonstrate that quantum information processing (QIP) completely rests on quantum Fourier transform (QFT), and 190 years after his death, the work of Jean-Baptiste Joseph Fourier is more present than ever in one of the most important pillars of physics: QIP. Specifically, this study shows the impact of QFT on the main tool of quantum communication: entanglement, with a particular emphasis on its spectral nature, whose study is completed when entanglement is used in teleportation, and quantum secret sharing. Finally, a better understanding of the spectral nature of quantum entanglement will lead to better protocols for quantum communications, in general, and quantum cryptography, in particular.
