11,244 research outputs found
The Path Integral for 1+1-dimensional QCD
We derive a path integral expression for the transition amplitude in
1+1-dimensional QCD starting from canonically quantized QCD. Gauge fixing after
quantization leads to a formulation in terms of gauge invariant but curvilinear
variables. Remainders of the curved space are Jacobians, an effective
potential, and sign factors just as for the problem of a particle in a box.
Based on this result we derive a Faddeev-Popov like expression for the
transition amplitude avoiding standard infinities that are caused by
integrations over gauge equivalent configurations.Comment: 16 pages, LaTeX, 3 PostScript figures, uses epsf.st
Separability and distillability in composite quantum systems -a primer-
Quantum mechanics is already 100 years old, but remains alive and full of
challenging open problems. On one hand, the problems encountered at the
frontiers of modern theoretical physics like Quantum Gravity, String Theories,
etc. concern Quantum Theory, and are at the same time related to open problems
of modern mathematics. But even within non-relativistic quantum mechanics
itself there are fundamental unresolved problems that can be formulated in
elementary terms. These problems are also related to challenging open questions
of modern mathematics; linear algebra and functional analysis in particular.
Two of these problems will be discussed in this article: a) the separability
problem, i.e. the question when the state of a composite quantum system does
not contain any quantum correlations or entanglement and b) the distillability
problem, i.e. the question when the state of a composite quantum system can be
transformed to an entangled pure state using local operations (local refers
here to component subsystems of a given system).
Although many results concerning the above mentioned problems have been
obtained (in particular in the last few years in the framework of Quantum
Information Theory), both problems remain until now essentially open. We will
present a primer on the current state of knowledge concerning these problems,
and discuss the relation of these problems to one of the most challenging
questions of linear algebra: the classification and characterization of
positive operator maps.Comment: 11 pages latex, 1 eps figure. Final version, to appear in J. Mod.
Optics, minor typos corrected, references adde
Back Reaction of Hawking Radiation on Black Hole Geometry
We propose a model for the geometry of a dynamical spherical shell in which
the metric is asymptotically Schwarzschild, but deviates from Ricci-flatness in
a finite neighbourhood of the shell. Hence, the geometry corresponds to a
`hairy' black hole, with the hair originating on the shell. The metric is
regular for an infalling shell, but it bifurcates, leading to two disconnected
Schwarzschild-like spacetime geometries. The shell is interpreted as either
collapsing matter or as Hawking radiation, depending on whether or not the
shell is infalling or outgoing. In this model, the Hawking radiation results
from tunnelling between the two geometries. Using this model, the back reaction
correction from Hawking radiation is calculated.Comment: Latex file, 15 pages, 4 figures enclosed, uses eps
Chemical Equilibrium in Collisions of Small Systems
The system-size dependence of particle production in heavy-ion collisions at
the top SPS energy is analyzed in terms of the statistical model. A systematic
comparison is made of two suppression mechanisms that quantify strange particle
yields in ultra-relativistic heavy-ion collisions: the canonical model with
strangeness correlation radius determined from the data and the model
formulated in the canonical ensemble using chemical off-equilibrium strangeness
suppression factor. The system-size dependence of the correlation radius and
the thermal parameters are obtained for p-p, C-C, Si-Si and Pb-Pb collisions at
sqrt(s_NN) = 17.3 AGeV. It is shown that on the basis of a consistent set of
data there is no clear difference between the two suppression patterns. In the
present study the strangeness correlation radius was found to exhibit a rather
weak dependence on the system size.Comment: 9 pages, 8 figures, submitted to Physical Review
An infrared diagnostic for magnetism in hot stars
Magnetospheric observational proxies are used for indirect detection of
magnetic fields in hot stars in the X-ray, UV, optical, and radio wavelength
ranges. To determine the viability of infrared (IR) hydrogen recombination
lines as a magnetic diagnostic for these stars, we have obtained low-resolution
(R~1200), near-IR spectra of the known magnetic B2V stars HR 5907 and HR 7355,
taken with the Ohio State Infrared Imager/Spectrometer (OSIRIS) attached to the
4.1m Southern Astrophysical Research (SOAR) Telescope. Both stars show definite
variable emission features in IR hydrogen lines of the Brackett series, with
similar properties as those found in optical spectra, including the derived
location of the detected magnetospheric plasma. These features also have the
added advantage of a lowered contribution of stellar flux at these wavelengths,
making circumstellar material more easily detectable. IR diagnostics will be
useful for the future study of magnetic hot stars, to detect and analyze
lower-density environments, and to detect magnetic candidates in areas obscured
from UV and optical observations, increasing the number of known magnetic stars
to determine basic formation properties and investigate the origin of their
magnetic fields.Comment: 4 pages, accepted for publication in A&
Quantum-state filtering applied to the discrimination of Boolean functions
Quantum state filtering is a variant of the unambiguous state discrimination
problem: the states are grouped in sets and we want to determine to which
particular set a given input state belongs.The simplest case, when the N given
states are divided into two subsets and the first set consists of one state
only while the second consists of all of the remaining states, is termed
quantum state filtering. We derived previously the optimal strategy for the
case of N non-orthogonal states, {|\psi_{1} >, ..., |\psi_{N} >}, for
distinguishing |\psi_1 > from the set {|\psi_2 >, ..., |\psi_N >} and the
corresponding optimal success and failure probabilities. In a previous paper
[PRL 90, 257901 (2003)], we sketched an appplication of the results to
probabilistic quantum algorithms. Here we fill in the gaps and give the
complete derivation of the probabilstic quantum algorithm that can optimally
distinguish between two classes of Boolean functions, that of the balanced
functions and that of the biased functions. The algorithm is probabilistic, it
fails sometimes but when it does it lets us know that it did. Our approach can
be considered as a generalization of the Deutsch-Jozsa algorithm that was
developed for the discrimination of balanced and constant Boolean functions.Comment: 8 page
Black Hole Entropy in the presence of Chern-Simons Terms
We derive a formula for the black hole entropy in theories with gravitational
Chern-Simons terms, by generalizing Wald's argument which uses the Noether
charge. It correctly reproduces the entropy of three-dimensional black holes in
the presence of Chern-Simons term, which was previously obtained via indirect
methods.Comment: v2: 12 pages, added reference
A Quantitative Measure of Interference
We introduce an interference measure which allows to quantify the amount of
interference present in any physical process that maps an initial density
matrix to a final density matrix. In particular, the interference measure
enables one to monitor the amount of interference generated in each step of a
quantum algorithm. We show that a Hadamard gate acting on a single qubit is a
basic building block for interference generation and realizes one bit of
interference, an ``i-bit''. We use the interference measure to quantify
interference for various examples, including Grover's search algorithm and
Shor's factorization algorithm. We distinguish between ``potentially
available'' and ``actually used'' interference, and show that for both
algorithms the potentially available interference is exponentially large.
However, the amount of interference actually used in Grover's algorithm is only
about 3 i-bits and asymptotically independent of the number of qubits, while
Shor's algorithm indeed uses an exponential amount of interference.Comment: 13 pages of latex; research done at http://www.quantware.ups-tlse.fr
Intercept-resend attacks in the Bennett-Brassard 1984 quantum key distribution protocol with weak coherent pulses
Unconditional security proofs of the Bennett-Brassard protocol of quantum key
distribution have been obtained recently. These proofs cover also practical
implementations that utilize weak coherent pulses in the four signal
polarizations. Proven secure rates leave open the possibility that new proofs
or new public discussion protocols obtain larger rates over increased distance.
In this paper we investigate limits to error rate and signal losses that can be
tolerated by future protocols and proofs.Comment: 11 pages, 3 figures. Version accepted for publication in Phys. Rev.
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