Quantum Fourier states and gates: teleportation via rough entanglement

Quantum Fourier gates (QFG) constitute a complete family of quantum gates that result from an exact combination of the quantum Fourier transform (QFT) and the SWAP gate. Therefore, the Feynman Gate constitutes the simplest example of this family, while the Bell states are the simplest cases of entangled states derived from the family. Moreover, this new tool will allow us to demonstrate that teleportation is not something that happens exclusively thanks to maximally and non-maximally entangled states, but that it is also possible with an incomplete form of entanglement known as rough entanglement. Finally, other applications necessary for the quantum Internet are incorporated.