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Quantum
Information and Computation
ISSN: 1533-7146
published since 2001
|
Vol.5 No.2 March 2005 |
New
construction of mutually unbiased bases in square dimensions
(pp093-101)
Pawel Wocjan and Thomas Beth
doi:
https://doi.org/10.26421/QIC5.2-1
Abstracts:
We show that k=w+2 mutually
unbiased bases can be constructed in any square dimension d=s^2 provided
that there are w mutually
orthogonal Latin squares of order s.
The construction combines the design-theoretic objects (s,k)-nets
(which can be constructed from w mutually
orthogonal Latin squares of order s and
vice versa) and generalized Hadamard matrices of size s. Using known
lower bounds on the asymptotic growth of the number of mutually
orthogonal Latin squares (based on number theoretic sieving techniques),
we obtain that the number of mutually unbiased bases in dimensions d=s^2 is
greater than s^{1/14.8} for
all s but
finitely many exceptions. Furthermore, our construction gives more
mutually unbiased bases in many non-prime-power dimensions than the
construction that reduces the problem to prime power dimensions.
Key words:
mutually unbiased bases, Latin squares,
design theory |
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