3,184 research outputs found
Quantum State Tomography of a Single Qubit: Comparison of Methods
The tomographic reconstruction of the state of a quantum-mechanical system is
an essential component in the development of quantum technologies. We present
an overview of different tomographic methods for determining the
quantum-mechanical density matrix of a single qubit: (scaled) direct inversion,
maximum likelihood estimation (MLE), minimum Fisher information distance, and
Bayesian mean estimation (BME). We discuss the different prior densities in the
space of density matrices, on which both MLE and BME depend, as well as ways of
including experimental errors and of estimating tomography errors. As a measure
of the accuracy of these methods we average the trace distance between a given
density matrix and the tomographic density matrices it can give rise to through
experimental measurements. We find that the BME provides the most accurate
estimate of the density matrix, and suggest using either the pure-state prior,
if the system is known to be in a rather pure state, or the Bures prior if any
state is possible. The MLE is found to be slightly less accurate. We comment on
the extrapolation of these results to larger systems.Comment: 15 pages, 4 figures, 2 tables; replaced previous figure 5 by new
table I. in Journal of Modern Optics, 201
Rotordynamic stability problems and solutions in high pressure turbocompressors
The stability of a high pressure compressor is investigated with special regard to the self-exciting effects in oil seals and labyrinths. It is shown how to stabilize a rotor in spite of these effects and even increase its stability with increasing pressure
Approximation Hardness of Graphic TSP on Cubic Graphs
We prove explicit approximation hardness results for the Graphic TSP on cubic
and subcubic graphs as well as the new inapproximability bounds for the
corresponding instances of the (1,2)-TSP. The proof technique uses new modular
constructions of simulating gadgets for the restricted cubic and subcubic
instances. The modular constructions used in the paper could be also of
independent interest
Tighter quantum uncertainty relations follow from a general probabilistic bound
Uncertainty relations (URs) like the Heisenberg-Robertson or the time-energy
UR are often considered to be hallmarks of quantum theory. Here, a simple
derivation of these URs is presented based on a single classical inequality
from estimation theory, a Cram\'er-Rao-like bound. The Heisenberg-Robertson UR
is then obtained by using the Born rule and the Schr\"odinger equation. This
allows a clear separtion of the probabilistic nature of quantum mechanics from
the Hilbert space structure and the dynamical law. It also simplifies the
interpretation of the bound. In addition, the Heisenberg-Robertson UR is
tightened for mixed states by replacing one variance by the so-called quantum
Fisher information. Thermal states of Hamiltonians with evenly-gapped energy
levels are shown to saturate the tighter bound for natural choices of the
operators. This example is further extended to Gaussian states of a harmonic
oscillator. For many-qubit systems, we illustrate the interplay between
entanglement and the structure of the operators that saturate the UR with
spin-squeezed states and Dicke states.Comment: 8 pages, 1 figure. v2: improved presentation, references added,
results on the connection between saturated inequality and entanglement
structure for multi-qubit states adde
Optimised surface-electrode ion-trap junctions for experiments with cold molecular ions
We discuss the design and optimisation of two types of junctions between
surface-electrode radiofrequency ion-trap arrays that enable the integration of
experiments with sympathetically cooled molecular ions on a monolithic chip
device. A detailed description of a multi-objective optimisation procedure
applicable to an arbitrary planar junction is presented, and the results for a
cross junction between four quadrupoles as well as a quadrupole-to-octupole
junction are discussed. Based on these optimised functional elements, we
propose a multi-functional ion-trap chip for experiments with translationally
cold molecular ions at temperatures in the millikelvin range. This study opens
the door to extending complex chip-based trapping techniques to
Coulomb-crystallised molecular ions with potential applications in mass
spectrometry, spectroscopy, controlled chemistry and quantum technology.Comment: 19 pages, 10 figure
New Inapproximability Bounds for TSP
In this paper, we study the approximability of the metric Traveling Salesman
Problem (TSP) and prove new explicit inapproximability bounds for that problem.
The best up to now known hardness of approximation bounds were 185/184 for the
symmetric case (due to Lampis) and 117/116 for the asymmetric case (due to
Papadimitriou and Vempala). We construct here two new bounded occurrence CSP
reductions which improve these bounds to 123/122 and 75/74, respectively. The
latter bound is the first improvement in more than a decade for the case of the
asymmetric TSP. One of our main tools, which may be of independent interest, is
a new construction of a bounded degree wheel amplifier used in the proof of our
results
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