6 research outputs found
Weak mutually unbiased bases
Quantum systems with variables in are considered. The
properties of lines in the phase space of
these systems, are studied. Weak mutually unbiased bases in these systems are
defined as bases for which the overlap of any two vectors in two different
bases, is equal to or alternatively to one of the
(where is a divisor of apart from ). They are designed for the
geometry of the phase space, in the sense
that there is a duality between the weak mutually unbiased bases and the
maximal lines through the origin. In the special case of prime , there are
no divisors of apart from and the weak mutually unbiased bases are
mutually unbiased bases
Partial ordering of weak mutually unbiased bases
YesA quantum system (n) with variables in Z(n), where n = Qpi (with pi prime numbers), is
considered. The non-near-linear geometry G(n) of the phase space Z(n) × Z(n), is studied. The
lines through the origin are factorized in terms of ‘prime factor lines’ in Z(pi)×Z(pi). Weak mutually
unbiased bases (WMUB) which are products of the mutually unbiased bases in the ‘prime factor
Hilbert spaces’ H(pi), are also considered. The factorization of both lines and WMUB is analogous
to the factorization of integers in terms of prime numbers. The duality between lines and WMUB is
discussed. It is shown that there is a partial order in the set of subgeometries of G(n), isomorphic
to the partial order in the set of subsystems of (n)