8,486 research outputs found
Linear resolutions of powers and products
The goal of this paper is to present examples of families of homogeneous
ideals in the polynomial ring over a field that satisfy the following
condition: every product of ideals of the family has a linear free resolution.
As we will see, this condition is strongly correlated to good primary
decompositions of the products and good homological and arithmetical properties
of the associated multi-Rees algebras. The following families will be discussed
in detail: polymatroidal ideals, ideals generated by linear forms and Borel
fixed ideals of maximal minors. The main tools are Gr\"obner bases and Sagbi
deformation
A Holographic Prediction of the Deconfinement Temperature
We argue that deconfinement in AdS/QCD models occurs via a first order
Hawking-Page type phase transition between a low temperature thermal AdS space
and a high temperature black hole. Such a result is consistent with the
expected temperature independence, to leading order in 1/N_c, of the meson
spectrum and spatial Wilson loops below the deconfinement temperature. As a
byproduct, we obtain model dependent deconfinement temperatures T_c in the hard
and soft wall models of AdS/QCD. Our result for T_c in the soft wall model is
close to a recent lattice prediction.Comment: 4 pages, 1 figure; v2 ref added, minor changes; v3 refs added,
discussion modified, to appear in PR
Optimum unambiguous discrimination of two mixed states and application to a class of similar states
We study the measurement for the unambiguous discrimination of two mixed
quantum states that are described by density operators and of
rank d, the supports of which jointly span a 2d-dimensional Hilbert space.
Based on two conditions for the optimum measurement operators, and on a
canonical representation for the density operators of the states, two equations
are derived that allow the explicit construction of the optimum measurement,
provided that the expression for the fidelity of the states has a specific
simple form. For this case the problem is mathematically equivalent to
distinguishing pairs of pure states, even when the density operators are not
diagonal in the canonical representation. The equations are applied to the
optimum unambiguous discrimination of two mixed states that are similar states,
given by , and that belong to the class where the
unitary operator U can be decomposed into multiple rotations in the d mutually
orthogonal two-dimensional subspaces determined by the canonical
representation.Comment: 8 pages, changes in title and presentatio
The method of global R* and its applications
The global R* operation is a powerful method for computing renormalisation
group functions. This technique, based on the principle of infrared
rearrangement, allows to express all the ultraviolet counterterms in terms of
massless propagator integrals. In this talk we present the main features of
global R* and its application to the renormalisation of QCD. By combining this
approach with the use of the program Forcer for the evaluation of the relevant
Feynman integrals, we renormalise for the first time QCD at five loops in
covariant gauges.Comment: 10 pages, 6 figures, contribution to the proceedings of the 13th
International Symposium on Radiative Corrections (RADCOR 2017
Optimum unambiguous discrimination of two mixed quantum states
We investigate generalized measurements, based on positive-operator-valued
measures, and von Neumann measurements for the unambiguous discrimination of
two mixed quantum states that occur with given prior probabilities. In
particular, we derive the conditions under which the failure probability of the
measurement can reach its absolute lower bound, proportional to the fidelity of
the states. The optimum measurement strategy yielding the fidelity bound of the
failure probability is explicitly determined for a number of cases. One example
involves two density operators of rank d that jointly span a 2d-dimensional
Hilbert space and are related in a special way. We also present an application
of the results to the problem of unambiguous quantum state comparison,
generalizing the optimum strategy for arbitrary prior probabilities of the
states.Comment: final versio
Discrimination of two mixed quantum states with maximum confidence and minimum probability of inconclusive results
We study an optimized measurement that discriminates two mixed quantum states
with maximum confidence for each conclusive result, thereby keeping the overall
probability of inconclusive results as small as possible. When the rank of the
detection operators associated with the two different conclusive outcomes does
not exceed unity we obtain a general solution. As an application, we consider
the discrimination of two mixed qubit states. Moreover, for the case of
higher-rank detection operators we give a solution for particular states. The
relation of the optimized measurement to other discrimination schemes is also
discussed.Comment: 7 pages, 1 figure, accepted for publication in Phys. Rev.
Programmable quantum state discriminators with simple programs
We describe a class of programmable devices that can discriminate between two
quantum states. We consider two cases. In the first, both states are unknown.
One copy of each of the unknown states is provided as input, or program, for
the two program registers, and the data state, which is guaranteed to be
prepared in one of the program states, is fed into the data register of the
device. This device will then tell us, in an optimal way, which of the
templates stored in the program registers the data state matches. In the second
case, we know one of the states while the other is unknown. One copy of the
unknown state is fed into the single program register, and the data state which
is guaranteed to be prepared in either the program state or the known state, is
fed into the data register. The device will then tell us, again optimally,
whether the data state matches the template or is the known state. We determine
two types of optimal devices. The first performs discrimination with minimum
error, the second performs optimal unambiguous discrimination. In all cases we
first treat the simpler problem of only one copy of the data state and then
generalize the treatment to n copies. In comparison to other works we find that
providing n > 1 copies of the data state yields higher success probabilities
than providing n > 1 copies of the program states.Comment: 17 pages, 5 figure
Spinning Dragging Strings
We use the AdS/CFT correspondence to compute the drag force experienced by a
heavy quark moving through a maximally supersymmetric SU(N) super Yang-Mills
plasma at nonzero temperature and R-charge chemical potential and at large 't
Hooft coupling. We resolve a discrepancy in the literature between two earlier
studies of such quarks. In addition, we consider small fluctuations of the
spinning strings dual to these probe quarks and find no evidence of
instabilities. We make some comments about suitable D7-brane boundary
conditions for the dual strings.Comment: 25 pages, 4 figures; v2 refs added; v3 to appear in JHEP, clarifying
comment
Powers of the vertex cover ideals
We describe a combinatorial condition on a graph which guarantees that all powers of its vertex cover ideal are componentwise linear. Then motivated by Eagon and Reiner's Theorem we study whether all powers of the vertex cover ideal of a Cohen-Macaulay graph have linear free resolutions. After giving a complete characterization of Cohen-Macaulay cactus graphs (i.e., connected graphs in which each edge belongs to at most one cycle) we show that all powers of their vertex cover ideals have linear resolutions
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