Multicomplementary operators via finite Fourier transform
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- 25 March 2005
- journal article
- research article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 38 (12) , 2747-2760
- https://doi.org/10.1088/0305-4470/38/12/015
Abstract
A complete set of d + 1 mutually unbiased bases exists in a Hilbert space of dimension d, whenever d is a power of a prime. We discuss a simple construction of d + 1 disjoint classes (each one having d - 1 commuting operators) such that the corresponding eigenstates form sets of unbiased bases. Such a construction works properly for prime dimension. We investigate an alternative construction in which the real numbers that label the classes are replaced by a finite field having d elements. One of these classes is diagonal, and can be mapped to cyclic operators by means of the finite Fourier transform, which allows one to understand complementarity in a similar way as for the position-momentum pair in standard quantum mechanics. The relevant examples of two and three qubits and two qutrits are discussed in detail.Keywords
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This publication has 27 references indexed in Scilit:
- Discrete phase space based on finite fieldsPhysical Review A, 2004
- Ascertaining the Values of,, andof a Polarization QubitPhysical Review Letters, 2003
- A New Proof for the Existence of Mutually Unbiased BasesAlgorithmica, 2002
- Quantum encodings in spin systems and harmonic oscillatorsPhysical Review A, 2002
- Mutually unbiased binary observable sets onNqubitsPhysical Review A, 2002
- Complementarity and certainty relations for two-dimensional systemsPhysical Review A, 2001
- Complementarity Enforced by Random Classical Phase KicksPhysical Review Letters, 1998
- Loss of coherence in interferometryPhysical Review A, 1993
- Complementary observables and uncertainty relationsPhysical Review D, 1987
- Geometrical description of quantal state determinationJournal of Physics A: General Physics, 1981