Quantum Fourier transform is the building block for creating entanglement

Abstract

This study demonstrates entanglement can be exclusively constituted by quantum Fourier transform (QFT) blocks. A bridge between entanglement and QFT will allow incorporating a spectral analysis to the already traditional temporal approach of entanglement, which will result in the development of new more performant, and fault-tolerant protocols to be used in quantum computing as well as quantum communication, with particular emphasis in the future quantum Internet.

Rough Entanglement: Not Enough Fourier

“…Moreover, between the preliminary works mentioned above [3][4][5][6] and the present study we will verify that the en- tanglement is organized in layers of QFT blocks and that a first layer (like the first cut of a distillation column) gives us a rustic version of entanglement, while a second layer (that is, through a complete distillation) gives us a maximally entangled version [1,[35][36][37] of the particles resulting from this process.…”

“…In previous works, [3][4][5][6] it was shown that quantum entanglement requires the intervention of two QFT blocks in its constitution. In this study, it is shown that the intervention of a single QFT block gives rise to a new type of entanglement with characteristics markedly differentiated from those present in its traditional forms, i.e., those manifested in the maximally entangled states, [1,47,48] and in the called nonmaximally entangled states.…”

“…[1] This powerful tool has been consolidated over the years in such critical applications as phase estimation, within the most famous quantum algorithm in the literature, the Shor algorithm. [2] In recent years, it has been shown that QFT is a key piece in the same constitution of quantum entanglement, [3][4][5][6] which is why the latter has two complementary facets, a temporal facet, traditionally known, [1] and another spectral, [3][4][5][6] which will lead to the creation of future algorithms and protocols with higher performance to be used in quantum communications, [7] in general, and quantum cryptography, [8] in particular.…”

“…The spectral manifestation of entanglement has been exploited to the limit in previous works in implementations ranging from quantum teleportation, [3][4][5][6] through quantum secret sharing (QSS), [3][4][5][6] to quantum repeaters. [3][4][5][6] These applications have a marked projection on the quantum key distribution (QKD) [9][10][11][12] protocols, although their greatest contribution is expected to happen in the field of the future quantum Internet.…”

“…The spectral manifestation of entanglement has been exploited to the limit in previous works in implementations ranging from quantum teleportation, [3][4][5][6] through quantum secret sharing (QSS), [3][4][5][6] to quantum repeaters. [3][4][5][6] These applications have a marked projection on the quantum key distribution (QKD) [9][10][11][12] protocols, although their greatest contribution is expected to happen in the field of the future quantum Internet. [13][14][15][16][17][18] Specifically, in the quantum cryptography [8] context, fiber optic cabling for terrestrial implementations of QKD protocols [9][10][11][12] requires quantum repeaters every certain number DOI: 10.1002/qute.202200176 of kilometers, [19,20] which in turn requires a large amount of quantum memory.…”