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Discrete phase-space structure of n-qubit mutually unbiased bases
KTH, School of Information and Communication Technology (ICT), Microelectronics and Information Technology, IMIT.ORCID iD: 0000-0002-2082-9583
2009 (English)In: Annals of Physics, ISSN 0003-4916, E-ISSN 1096-035X, Vol. 324, no 1, 53-72 p.Article in journal (Refereed) Published
Abstract [en]

We work out the phase-space structure for a system of n qubits. We replace the field of real numbers that label the axes of the continuous phase space by the finite field GF(2(n)) and investigate the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We provide a simple classification of such curves and study in detail the four- and eight-dimensional cases, analyzing also the effect of local transformations. In this way, we provide a comprehensive phase-space approach to the construction of mutually unbiased bases for n qubits.

Place, publisher, year, edition, pages
2009. Vol. 324, no 1, 53-72 p.
Keyword [en]
Mutually unbiased bases, Discrete phase space, Galois fields, quantum-state tomography, prime power dimensions, mean kings problem, wigner-function, hilbert-space, systems, weyl, geometries, mechanics, codes
URN: urn:nbn:se:kth:diva-18217DOI: 10.1016/j.aop.2008.10.003ISI: 000263807600005ScopusID: 2-s2.0-59849125581OAI: diva2:336263
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2011-01-31Bibliographically approved

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