275 research outputs found
On local invariants of pure three-qubit states
We study invariants of three-qubit states under local unitary
transformations, i.e. functions on the space of entanglement types, which is
known to have dimension 6. We show that there is no set of six independent
polynomial invariants of degree less than or equal to 6, and find such a set
with maximum degree 8. We describe an intrinsic definition of a canonical state
on each orbit, and discuss the (non-polynomial) invariants associated with it.Comment: LateX, 13 pages. Minor typoes corrected. Published versio
Fast simulation of stabilizer circuits using a graph state representation
According to the Gottesman-Knill theorem, a class of quantum circuits, namely
the so-called stabilizer circuits, can be simulated efficiently on a classical
computer. We introduce a new algorithm for this task, which is based on the
graph-state formalism. It shows significant improvement in comparison to an
existing algorithm, given by Gottesman and Aaronson, in terms of speed and of
the number of qubits the simulator can handle. We also present an
implementation.Comment: v2: significantly improved presentation; accepted by PR
Multiparticle entanglement purification for two-colorable graph states
We investigate multiparticle entanglement purification schemes which allow
one to purify all two colorable graph states, a class of states which includes
e.g. cluster states, GHZ states and codewords of various error correction
codes. The schemes include both recurrence protocols and hashing protocols. We
analyze these schemes under realistic conditions and observe for a generic
error model that the threshold value for imperfect local operations depends on
the structure of the corresponding interaction graph, but is otherwise
independent of the number of parties. The qualitative behavior can be
understood from an analytically solvable model which deals only with a
restricted class of errors. We compare direct multiparticle entanglement
purification protocols with schemes based on bipartite entanglement
purification and show that the direct multiparticle entanglement purification
is more efficient and the achievable fidelity of the purified states is larger.
We also show that the purification protocol allows one to produce private
entanglement, an important aspect when using the produced entangled states for
secure applications. Finally we discuss an experimental realization of a
multiparty purification protocol in optical lattices which is issued to improve
the fidelity of cluster states created in such systems.Comment: 22 pages, 8 figures; replaced with published versio
Three-qubit pure-state canonical forms
In this paper we analyze the canonical forms into which any pure three-qubit
state can be cast. The minimal forms, i.e. the ones with the minimal number of
product states built from local bases, are also presented and lead to a
complete classification of pure three-qubit states. This classification is
related to the values of the polynomial invariants under local unitary
transformations by a one-to-one correspondence.Comment: REVTEX, 9 pages, 1 figur
B4galnt2-mediated host glycosylation influences the susceptibility to Citrobacter rodentium infection
Histo-blood group antigens in the intestinal mucosa play important roles in host-microbe interactions and modulate the susceptibility to enteric pathogens. The B4galnt2 gene, expressed in the GI tract of most mammals, including humans, encodes a beta-1,4-N-acetylgalactosaminyltransferase enzyme which catalyzes the last step in the biosynthesis of the Sd(a) and Cad blood group antigens by adding an N-acetylgalactosamine (GalNAc) residue to the precursor molecules. In our study, we found that loss of B4galnt2 expression is associated with increased susceptibility to Citrobacter rodentium infection, a murine model pathogen for human enteropathogenic Escherichia coli. We observed increased histopathological changes upon C. rodentium infection in mice lacking B4galnt2 compared to B4galnt2-expressing wild-type mice. In addition, wild-type mice cleared the C. rodentium infection faster than B4galnt2(-/-) knockout mice. It is known that C. rodentium uses its type 1 fimbriae adhesive subunit to bind specifically to D-mannose residues on mucosal cells. Flow cytometry analysis of intestinal epithelial cells showed the absence of GalNAc-modified glycans but an increase in mannosylated glycans in B4galnt2-deficient mice compared to B4galnt2-sufficient mice. Adhesion assays using intestinal epithelial organoid-derived monolayers revealed higher C. rodentium adherence to cells lacking B4galnt2 expression compared to wild-type cells which in turn was reduced in the absence of type I fimbriae. In summary, we show that B4galnt2 expression modulates the susceptibility to C. rodentium infection, which is partly mediated by fimbriae-mannose interaction
The Lie Algebraic Significance of Symmetric Informationally Complete Measurements
Examples of symmetric informationally complete positive operator valued
measures (SIC-POVMs) have been constructed in every dimension less than or
equal to 67. However, it remains an open question whether they exist in all
finite dimensions. A SIC-POVM is usually thought of as a highly symmetric
structure in quantum state space. However, its elements can equally well be
regarded as a basis for the Lie algebra gl(d,C). In this paper we examine the
resulting structure constants, which are calculated from the traces of the
triple products of the SIC-POVM elements and which, it turns out, characterize
the SIC-POVM up to unitary equivalence. We show that the structure constants
have numerous remarkable properties. In particular we show that the existence
of a SIC-POVM in dimension d is equivalent to the existence of a certain
structure in the adjoint representation of gl(d,C). We hope that transforming
the problem in this way, from a question about quantum state space to a
question about Lie algebras, may help to make the existence problem tractable.Comment: 56 page
Local symmetry properties of pure 3-qubit states
Entanglement types of pure states of 3 qubits are classified by means of
their stabilisers in the group of local unitary operations. It is shown that
the stabiliser is generically discrete, and that a larger stabiliser indicates
a stationary value for some local invariant. We describe all the exceptional
states with enlarged stabilisers.Comment: 32 pages, 5 encapsulated PostScript files for 3 figures. Published
version, with minor correction
Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
We investigate the average bipartite entanglement, over all possible
divisions of a multipartite system, as a useful measure of multipartite
entanglement. We expose a connection between such measures and
quantum-error-correcting codes by deriving a formula relating the weight
distribution of the code to the average entanglement of encoded states.
Multipartite entangling power of quantum evolutions is also investigated.Comment: 13 pages, 1 figur
Global entanglement in multiparticle systems
We define a polynomial measure of multiparticle entanglement which is
scalable, i.e., which applies to any number of spin-1/2 particles. By
evaluating it for three particle states, for eigenstates of the one dimensional
Heisenberg antiferromagnet and on quantum error correcting code subspaces, we
illustrate the extent to which it quantifies global entanglement. We also apply
it to track the evolution of entanglement during a quantum computation.Comment: 9 pages, plain TeX, 1 PostScript figure included with epsf.tex
(ignore the under/overfull \vbox error messages); for related work see
http://math.ucsd.edu/~dmeyer/research.html or
http://www.math.ucsd.edu/~nwallach
Distributed Entanglement
Consider three qubits A, B, and C which may be entangled with each other. We
show that there is a trade-off between A's entanglement with B and its
entanglement with C. This relation is expressed in terms of a measure of
entanglement called the "tangle," which is related to the entanglement of
formation. Specifically, we show that the tangle between A and B, plus the
tangle between A and C, cannot be greater than the tangle between A and the
pair BC. This inequality is as strong as it could be, in the sense that for any
values of the tangles satisfying the corresponding equality, one can find a
quantum state consistent with those values. Further exploration of this result
leads to a definition of the "three-way tangle" of the system, which is
invariant under permutations of the qubits.Comment: 13 pages LaTeX; references added, derivation of Eq. (11) simplifie
- …