Natural majorization of the Quantum Fourier Transformation in phase-estimation algorithms
| dc.creator | Orus, Roman | |
| dc.creator | Latorre, Jose I. | |
| dc.creator | Martin-Delgado, Miguel A. | |
| dc.date | 2002-06-19 | |
| dc.date | 2003-03-28 | |
| dc.date.accessioned | 2026-07-07T06:04:26Z | |
| dc.date.available | 2026-07-07T06:04:26Z | |
| dc.description | We prove that majorization relations hold step by step in the Quantum Fourier Transformation (QFT) for phase-estimation algorithms considered in the canonical decomposition. Our result relies on the fact that states which are mixed by Hadamard operators at any stage of the computation only differ by a phase. This property is a consequence of the structure of the initial state and of the QFT, based on controlled-phase operators and a single action of a Hadamard gate per qubit. As a consequence, Hadamard gates order the probability distribution associated to the quantum state, whereas controlled-phase operators carry all the entanglement but are immaterial to majorization. We also prove that majorization in phase-estimation algorithms follows in a most natural way from unitary evolution, unlike its counterpart in Grover's algorithm. | |
| dc.description | LaTeX, 19 pages, 2 figures, minor corrections added | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0206134 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0206134 | |
| dc.identifier | Quantum Information Processing 1 (4): 283-302 (2002) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/90297 | |
| dc.subject | Quantum Physics | |
| dc.title | Natural majorization of the Quantum Fourier Transformation in phase-estimation algorithms | |
| dc.type | text |