3,091 research outputs found
Computation-free presentation of the fundamental group of generic -torus curves
In this note, we present a new method for computing fundamental groups of
curve complements using a variation of the Zariski-Van Kampen method on general
ruled surfaces. As an application we give an alternative (computation-free)
proof for the fundamental group of generic -torus curves.Comment: 7 pages, 3 figure
Structure of semisimple Hopf algebras of dimension
Let be prime numbers with , and an algebraically closed
field of characteristic 0. We show that semisimple Hopf algebras of dimension
can be constructed either from group algebras and their duals by means
of extensions, or from Radford biproduct R#kG, where is the group
algebra of group of order , is a semisimple Yetter-Drinfeld Hopf
algebra in of dimension . As an application,
the special case that the structure of semisimple Hopf algebras of dimension
is given.Comment: 11pages, to appear in Communications in Algebr
Quantum nonlocality in the presence of superselection rules and data hiding protocols
We consider a quantum system subject to superselection rules, for which
certain restrictions apply to the quantum operations that can be implemented.
It is shown how the notion of quantum-nonlocality has to be redefined in the
presence of superselection rules: there exist separable states that cannot be
prepared locally and exhibit some form of nonlocality. Moreover, the notion of
local distinguishability in the presence of classical communication has to be
altered. This can be used to perform quantum information tasks that are
otherwise impossible. In particular, this leads to the introduction of perfect
quantum data hiding protocols, for which quantum communication (eventually in
the form of a separable but nonlocal state) is needed to unlock the secret.Comment: 4 page
Characterizing Entanglement via Uncertainty Relations
We derive a family of necessary separability criteria for finite-dimensional
systems based on inequalities for variances of observables. We show that every
pure bipartite entangled state violates some of these inequalities.
Furthermore, a family of bound entangled states and true multipartite entangled
states can be detected. The inequalities also allow to distinguish between
different classes of true tripartite entanglement for qubits. We formulate an
equivalent criterion in terms of covariance matrices. This allows us to apply
criteria known from the regime of continuous variables to finite-dimensional
systems.Comment: 4 pages, no figures. v2: Some discussion added, main results
unchange
The Majorization Arrow in Quantum Algorithm Design
We apply majorization theory to study the quantum algorithms known so far and
find that there is a majorization principle underlying the way they operate.
Grover's algorithm is a neat instance of this principle where majorization
works step by step until the optimal target state is found. Extensions of this
situation are also found in algorithms based in quantum adiabatic evolution and
the family of quantum phase-estimation algorithms, including Shor's algorithm.
We state that in quantum algorithms the time arrow is a majorization arrow.Comment: REVTEX4.b4 file, 4 color figures (typos corrected.
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