Rough Entanglement: Not Enough Fourier

This work presents a new form of entanglement known as rough entanglement. It is based on the quantum Fourier transform (QFT) and is an alternative to those used in quantum information processing for generating maximally and nonmaximally entangled states. The roughly entangled pairs are used in the quantum teleportation protocol, where, the performance achieved in the reconstruction of the teleported state is evaluated. The aforementioned teleportation is implemented on a simulator and a 5-qubit physical machine from the IBM Q Experience inventory. Emphasis is placed on the teleportation of computational basis states (CBS) commonly used in quantum key distribution protocols. Finally, in previous works, it is shown that to generate Bell states the intervention of two QFT blocks is required, while the rough version requires only one. The lack of a second layer or QFT block in its constitution gives the name to this new type of entanglement.