Seyfarth, Ulrich ; Ranade, Kedar (2011)
Construction of mutually unbiased bases with cyclic symmetry for qubit systems.
In: Physical Review A, 84 (4)
doi: 10.1103/PhysRevA.84.042327
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
For the complete estimation of arbitrary unknown quantum states by measurements, the use of mutually unbiased bases has been well established in theory and experiment for the past 20 years. However, most constructions of these bases make heavy use of abstract algebra and the mathematical theory of finite rings and fields, and no simple and generally accessible construction is available. This is particularly true in the case of a system composed of several qubits, which is arguably the most important case in quantum information science and quantum computation. In this paper, we close this gap by providing a simple and straightforward method for the construction of mutually unbiased bases in the case of a qubit register. We show that our construction is also accessible to experiments, since only Hadamard and controlled-phase gates are needed, which are available in most practical realizations of a quantum computer. Moreover, our scheme possesses the optimal scaling possible, i.e., the number of gates scales only linearly in the number of qubits.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2011 |
| Autor(en): | Seyfarth, Ulrich ; Ranade, Kedar |
| Art des Eintrags: | Bibliographie |
| Titel: | Construction of mutually unbiased bases with cyclic symmetry for qubit systems |
| Sprache: | Englisch |
| Publikationsjahr: | Oktober 2011 |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Physical Review A |
| Jahrgang/Volume einer Zeitschrift: | 84 |
| (Heft-)Nummer: | 4 |
| DOI: | 10.1103/PhysRevA.84.042327 |
| Zugehörige Links: | |
| Kurzbeschreibung (Abstract): | For the complete estimation of arbitrary unknown quantum states by measurements, the use of mutually unbiased bases has been well established in theory and experiment for the past 20 years. However, most constructions of these bases make heavy use of abstract algebra and the mathematical theory of finite rings and fields, and no simple and generally accessible construction is available. This is particularly true in the case of a system composed of several qubits, which is arguably the most important case in quantum information science and quantum computation. In this paper, we close this gap by providing a simple and straightforward method for the construction of mutually unbiased bases in the case of a qubit register. We show that our construction is also accessible to experiments, since only Hadamard and controlled-phase gates are needed, which are available in most practical realizations of a quantum computer. Moreover, our scheme possesses the optimal scaling possible, i.e., the number of gates scales only linearly in the number of qubits. |
| Freie Schlagworte: | Secure Data |
| ID-Nummer: | TUD-CS-2011-0251 |
| Fachbereich(e)/-gebiet(e): | LOEWE LOEWE > LOEWE-Zentren Zentrale Einrichtungen LOEWE > LOEWE-Zentren > CASED – Center for Advanced Security Research Darmstadt Zentrale Einrichtungen > Universitäts- und Landesbibliothek (ULB) |
| Hinterlegungsdatum: | 30 Dez 2016 20:23 |
| Letzte Änderung: | 03 Jul 2020 09:08 |
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