1,035 research outputs found
All degree six local unitary invariants of k qudits
We give explicit index-free formulae for all the degree six (and also degree
four and two) algebraically independent local unitary invariant polynomials for
finite dimensional k-partite pure and mixed quantum states. We carry out this
by the use of graph-technical methods, which provides illustrations for this
abstract topic.Comment: 18 pages, 6 figures, extended version. Comments are welcom
Model-independent resonance parameter extraction using the trace of K and T matrices
A model-independent method for the determination of Breit-Wigner resonance
parameters is presented. The method is based on eliminating the dependence on
the choice of channel basis by analyzing the trace of the K and T matrices in
the coupled-channel formalism, rather than individual matrix elements of the
multichannel scattering matrix.Comment: 6 pages, 16 figure
Three fermions with six single particle states can be entangled in two inequivalent ways
Using a generalization of Cayley's hyperdeterminant as a new measure of
tripartite fermionic entanglement we obtain the SLOCC classification of
three-fermion systems with six single particle states. A special subclass of
such three-fermion systems is shown to have the same properties as the
well-known three-qubit ones. Our results can be presented in a unified way
using Freudenthal triple systems based on cubic Jordan algebras. For systems
with an arbitrary number of fermions and single particle states we propose the
Pl\"ucker relations as a sufficient and necessary condition of separability.Comment: 23 pages LATE
On the algebra of local unitary invariants of pure and mixed quantum states
We study the structure of the inverse limit of the graded algebras of local
unitary invariant polynomials using its Hilbert series. For k subsystems, we
conjecture that the inverse limit is a free algebra and the number of
algebraically independent generators with homogenous degree 2m equals the
number of conjugacy classes of index m subgroups in a free group on k-1
generators.
Similarly, we conjecture that the inverse limit in the case of k-partite
mixed state invariants is free and the number of algebraically independent
generators with homogenous degree m equals the number of conjugacy classes of
index m subgroups in a free group on k generators. The two conjectures are
shown to be equivalent.
To illustrate the equivalence, using the representation theory of the unitary
groups, we obtain all invariants in the m=2 graded parts and express them in a
simple form both in the case of mixed and pure states. The transformation
between the two forms is also derived. Analogous invariants of higher degree
are also introduced.Comment: 14 pages, no figure
Delta rho pi interaction leading to N* and Delta* resonances
We have performed a calculation for the three body system
by using the fixed center approximation to Faddeev equations, taking the
interaction between and , and, and and
from the chiral unitary approach. We find several peaks in the modulus
squared of the three-body scattering amplitude, indicating the existence of
resonances, which can be associated to known and and baryon states.Comment: Presented at the 21st European Conference on Few-Body Problems in
Physics, Salamanca, Spain, 30 August - 3 September 201
The Veldkamp space of multiple qubits
We introduce a point-line incidence geometry in which the commutation
relations of the real Pauli group of multiple qubits are fully encoded. Its
points are pairs of Pauli operators differing in sign and each line contains
three pairwise commuting operators any of which is the product of the other two
(up to sign).
We study the properties of its Veldkamp space enabling us to identify subsets
of operators which are distinguished from the geometric point of view. These
are geometric hyperplanes and pairwise intersections thereof.
Among the geometric hyperplanes one can find the set of self-dual operators
with respect to the Wootters spin-flip operation well-known from studies
concerning multiqubit entanglement measures. In the two- and three-qubit cases
a class of hyperplanes gives rise to Mermin squares and other generalized
quadrangles. In the three-qubit case the hyperplane with points corresponding
to the 27 Wootters self-dual operators is just the underlying geometry of the
E6(6) symmetric entropy formula describing black holes and strings in five
dimensions.Comment: 15 pages, 1 figure; added references, corrected typos; minor change
Association between exposure-relevant polymorphisms in CYP1B1, EPHX1, NQO1, GSTM1, GSTP1 and GSTT1 and risk of colorectal cancer in a Czech population
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