2,501 research outputs found
Affine Constellations Without Mutually Unbiased Counterparts
It has been conjectured that a complete set of mutually unbiased bases in a
space of dimension d exists if and only if there is an affine plane of order d.
We introduce affine constellations and compare their existence properties with
those of mutually unbiased constellations, mostly in dimension six. The
observed discrepancies make a deeper relation between the two existence
problems unlikely.Comment: 8 page
On the Cohomology of Contextuality
Recent work by Abramsky and Brandenburger used sheaf theory to give a
mathematical formulation of non-locality and contextuality. By adopting this
viewpoint, it has been possible to define cohomological obstructions to the
existence of global sections. In the present work, we illustrate new insights
into different aspects of this theory. We shed light on the power of detection
of the cohomological obstruction by showing that it is not a complete invariant
for strong contextuality even under symmetry and connectedness restrictions on
the measurement cover, disproving a previous conjecture. We generalise
obstructions to higher cohomology groups and show that they give rise to a
refinement of the notion of cohomological contextuality: different "levels" of
contextuality are organised in a hierarchy of logical implications. Finally, we
present an alternative description of the first cohomology group in terms of
torsors, resulting in a new interpretation of the cohomological obstructions.Comment: In Proceedings QPL 2016, arXiv:1701.0024
Correlations in optically-controlled quantum emitters
We address the problem of optically controlling and quantifying the
dissipative dynamics of quantum and classical correlations in a set-up of
individual quantum emitters under external laser excitation. We show that both
types of correlations, the former measured by the quantum discord, are present
in the system's evolution even though the emitters may exhibit an early stage
disentanglement. In the absence of external laser pumping,we demonstrate
analytically, for a set of suitable initial states, that there is an entropy
bound for which quantum discord and entanglement of the emitters are always
greater than classical correlations, thus disproving an early conjecture that
classical correlations are greater than quantum correlations. Furthermore, we
show that quantum correlations can also be greater than classical correlations
when the system is driven by a laser field. For scenarios where the emitters'
quantum correlations are below their classical counterparts, an optimization of
the evolution of the quantum correlations can be carried out by appropriately
tailoring the amplitude of the laser field and the emitters' dipole-dipole
interaction. We stress the importance of using the entanglement of formation,
rather than the concurrence, as the entanglement measure, since the latter can
grow beyond the total correlations and thus give incorrect results on the
actual system's degree of entanglement.Comment: 11 pages, 10 figures, this version contains minor modifications; to
appear in Phys. Rev.
Some open questions in "wave chaos"
The subject area referred to as "wave chaos", "quantum chaos" or "quantum
chaology" has been investigated mostly by the theoretical physics community in
the last 30 years. The questions it raises have more recently also attracted
the attention of mathematicians and mathematical physicists, due to connections
with number theory, graph theory, Riemannian, hyperbolic or complex geometry,
classical dynamical systems, probability etc. After giving a rough account on
"what is quantum chaos?", I intend to list some pending questions, some of them
having been raised a long time ago, some others more recent
Challenging computations of Hilbert bases of cones associated with algebraic statistics
In this paper we present two independent computational proofs that the monoid
derived from contingency tables is normal, completing the
classification by Hibi and Ohsugi. We show that Vlach's vector disproving
normality for the monoid derived from contingency tables is
the unique minimal such vector up to symmetry. Finally, we compute the full
Hilbert basis of the cone associated with the non-normal monoid of the
semi-graphoid for . The computations are based on extensions of the
packages LattE-4ti2 and Normaliz.Comment: 10 page
BMN Gauge Theory as a Quantum Mechanical System
We rigorously derive an effective quantum mechanical Hamiltonian from N=4
gauge theory in the BMN limit. Its eigenvalues yield the exact one-loop
anomalous dimensions of scalar two-impurity BMN operators for all genera. It is
demonstrated that this reformulation vastly simplifies computations. E.g. the
known anomalous dimension formula for genus one is reproduced through a
one-line calculation. We also efficiently evaluate the genus two correction,
finding a non-vanishing result. We comment on multi-trace two-impurity
operators and we conjecture that our quantum-mechanical reformulation could be
extended to higher quantum loops and more impurities.Comment: 13 pages, v2: minor changes, v3: typo corrected, to appear in Phys.
Lett.
The slicing number of a knot
An open question asks if every knot of 4-genus g_s can be changed into a
slice knot by g_s crossing changes. A counterexample is given.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-41.abs.html Version 3:
reference to Murakami and Yasuhara adde
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