22 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
Low-Temperature Specific Heat of an Extreme-Type-II Superconductor at High Magnetic Fields
We present a detailed study of the quasiparticle contribution to the
low-temperature specific heat of an extreme type-II superconductor at high
magnetic fields. Within a T-matrix approximation for the self-energies in the
mixed state of a homogeneous superconductor, the electronic specific heat is a
linear function of temperature with a linear- coefficient
being a nonlinear function of magnetic field . In the range of magnetic
fields H\agt (0.15-0.2)H_{c2} where our theory is applicable, the calculated
closely resembles the experimental data for the borocarbide
superconductor YNiBC.Comment: 7 pages, 2 figures, to appear in Physical Review
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)
An analytic function approach to weak mutually unbiased bases
yesQuantum systems with variables in Z(d) are considered, and three different structures are studied. The first is weak mutually unbiased bases, ... The second is maximal lines through the origin in the Z(d)×Z(d) phase space. The third is an analytic representation in the complex plane based on Theta functions, and their zeros. It is shown that there is a correspondence (triality) that links strongly these three apparently different structures. For simplicity, the case where d=p1×p2, where p1,p2 are odd prime numbers different from each other, is considered.The full text will be available 12 months after publicatio
Mutually unbiased projectors and duality between lines and bases in finite quantum systems
Quantum systems with variables in the ring Z(d) are considered, and the concepts of weak mutually unbiased bases and mutually unbiased projectors are discussed. The lines through the origin in the Z(d) x Z(d) phase space, are classified into maximal lines (sets of d points), and sublines (sets of d(i) points where d(i)vertical bar d). The sublines are intersections of maximal lines. It is shown that there exists a duality between the properties of lines (resp., sublines), and the properties of weak mutually unbiased bases (resp., mutually unbiased projectors)