795 research outputs found
Local unitary invariants for multipartite quantum systems
A method is presented to obtain local unitary invariants for multipartite
quantum systems consisting of fermions or distinguishable particles. The
invariants are organized into infinite families, in particular, the
generalization to higher dimensional single particle Hilbert spaces is
straightforward. Many well-known invariants and their generalizations are also
included.Comment: 13 page
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
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
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
Genotype and haplotype analysis of TP53 gene and the risk of pancreatic cancer: An association study in the Czech Republic
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