2,980 research outputs found
Local antimagic chromatic number of partite graphs
Let be a connected graph with and . A bijection
is called a local antimagic labeling of if
for any two adjacent vertices and , , where , and is the set of edges incident to . Thus,
any local antimagic labeling induces a proper vertex coloring of where the
vertex is assigned the color . The local antimagic chromatic number
is the minimum number of colors taken over all colorings induced by local
antimagic labelings of . Let . In this paper, the local antimagic
chromatic number of a complete tripartite graph , and copies of
a complete bipartite graph where are
determined
Non-locality and Communication Complexity
Quantum information processing is the emerging field that defines and
realizes computing devices that make use of quantum mechanical principles, like
the superposition principle, entanglement, and interference. In this review we
study the information counterpart of computing. The abstract form of the
distributed computing setting is called communication complexity. It studies
the amount of information, in terms of bits or in our case qubits, that two
spatially separated computing devices need to exchange in order to perform some
computational task. Surprisingly, quantum mechanics can be used to obtain
dramatic advantages for such tasks.
We review the area of quantum communication complexity, and show how it
connects the foundational physics questions regarding non-locality with those
of communication complexity studied in theoretical computer science. The first
examples exhibiting the advantage of the use of qubits in distributed
information-processing tasks were based on non-locality tests. However, by now
the field has produced strong and interesting quantum protocols and algorithms
of its own that demonstrate that entanglement, although it cannot be used to
replace communication, can be used to reduce the communication exponentially.
In turn, these new advances yield a new outlook on the foundations of physics,
and could even yield new proposals for experiments that test the foundations of
physics.Comment: Survey paper, 63 pages LaTeX. A reformatted version will appear in
Reviews of Modern Physic
Quantum Circuits for Measuring Levin-Wen Operators
We construct quantum circuits for measuring the commuting set of vertex and
plaquette operators that appear in the Levin-Wen model for doubled Fibonacci
anyons. Such measurements can be viewed as syndrome measurements for the
quantum error-correcting code defined by the ground states of this model (the
Fibonacci code). We quantify the complexity of these circuits with gate counts
using different universal gate sets and find these measurements become
significantly easier to perform if n-qubit Toffoli gates with n = 3,4 and 5 can
be carried out directly. In addition to measurement circuits, we construct
simplified quantum circuits requiring only a few qubits that can be used to
verify that certain self-consistency conditions, including the pentagon
equation, are satisfied by the Fibonacci code.Comment: 12 pages, 13 figures; published versio
On certain families of planar patterns and fractals
This survey article is dedicated to some families of fractals that were
introduced and studied during the last decade, more precisely, families of
Sierpi\'nski carpets: limit net sets, generalised Sierpi\'nski carpets and
labyrinth fractals. We give a unifying approach of these fractals and several
of their topological and geometrical properties, by using the framework of
planar patterns.Comment: survey article, 10 pages, 7 figure
Liberation of orthogonal Lie groups
We show that under suitable assumptions, we have a one-to-one correspondence
between classical groups and free quantum groups, in the compact orthogonal
case. We classify the groups under correspondence, with the result that there
are exactly 6 of them: . We investigate the
representation theory aspects of the correspondence, with the result that for
, this is compatible with the Bercovici-Pata bijection.
Finally, we discuss some more general classification problems in the compact
orthogonal case, notably with the construction of a new quantum group.Comment: 42 page
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