17,941 research outputs found
Quantum measurements with prescribed symmetry
We introduce a method to determine whether a given generalised quantum
measurement is isolated or it belongs to a family of measurements having the
same prescribed symmetry. The technique proposed reduces to solving a linear
system of equations in some relevant cases. As consequence, we provide a simple
derivation of the maximal family of Symmetric Informationally Complete
measurements (SIC)-POVM in dimension 3. Furthermore, we show that the following
remarkable geometrical structures are isolated, so that free parameters cannot
be introduced: (a) maximal sets of mutually unbiased bases in prime power
dimensions from 4 to 16, (b) SIC-POVM in dimensions from 4 to 16 and (c)
contextuality Kochen-Specker sets in dimension 3, 4 and 6, composed of 13, 18
and 21 vectors, respectively.Comment: 10 pages, 2 figure
Bott - Borel - Weil Construction For Quantum Supergroup Uq(gl(m|n))
The finite dimensional irreducible representations of the quantum supergroup
are constructed geometrically using techniques from the Bott -
Borel - Weil theory and vector coherent states.Comment: Latex, 22 page
Extreme points of the set of density matrices with positive partial transpose
We present a necessary and sufficient condition for a finite dimensional
density matrix to be an extreme point of the convex set of density matrices
with positive partial transpose with respect to a subsystem. We also give an
algorithm for finding such extreme points and illustrate this by some examples.Comment: 4 pages, 2 figure
Discrete phase-space structure of -qubit mutually unbiased bases
We work out the phase-space structure for a system of qubits. We replace
the field of real numbers that label the axes of the continuous phase space by
the finite field \Gal{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
qubits.Comment: Title changed. Improved version. Accepted for publication in Annals
of Physic
On the irreducible components of moduli schemes for affine spherical varieties
We give a combinatorial description of all affine spherical varieties with
prescribed weight monoid . As an application, we obtain a
characterization of the irreducible components of Alexeev and Brion's moduli
scheme for such varieties. Moreover, we find several
sufficient conditions for to be irreducible and exhibit
several examples where is reducible. Finally, we provide
examples of non-reduced .Comment: v4: 26 pages, final versio
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