467 research outputs found
Unsolvability of the Halting Problem in Quantum Dynamics
It is shown that the halting problem cannot be solved consistently in both
the Schrodinger and Heisenberg pictures of quantum dynamics. The existence of
the halting machine, which is assumed from quantum theory, leads into a
contradiction when we consider the case when the observer's reference frame is
the system that is to be evolved in both pictures. We then show that in order
to include the evolution of observer's reference frame in a physically sensible
way, the Heisenberg picture with time going backwards yields a correct
description.Comment: 4 pages, 3 figure
Comment on "The black hole final state"
Horowitz and Maldacena have suggested that the unitarity of the black hole
S-matrix can be reconciled with Hawking's semiclassical arguments if a
final-state boundary condition is imposed at the spacelike singularity inside
the black hole. We point out that, in this scenario, departures from unitarity
can arise due to interactions between the collapsing body and the infalling
Hawking radiation inside the event horizon. The amount of information lost when
a black hole evaporates depends on the extent to which these interactions are
entangling.Comment: 4 pages, REVTe
Scaling issues in ensemble implementations of the Deutsch-Jozsa algorithm
We discuss the ensemble version of the Deutsch-Jozsa (DJ) algorithm which
attempts to provide a "scalable" implementation on an expectation-value NMR
quantum computer. We show that this ensemble implementation of the DJ algorithm
is at best as efficient as the classical random algorithm. As soon as any
attempt is made to classify all possible functions with certainty, the
implementation requires an exponentially large number of molecules. The
discrepancies arise out of the interpretation of mixed state density matrices.Comment: Minor changes, reference added, replaced with publised versio
Use of geostatistical Bayesian updating to integrate airborne radiometrics and soil geochemistry to improve mapping for mineral exploration
Mineral exploration programmes around the world use data from remote
sensing, geophysics, and direct sampling. On a regional scale, the
combination of airborne geophysics and ground-based geochemical
sampling can aid geological mapping and mineral exploration. Since
airborne geophysical and traditional soil-sampling data are generated at
different spatial resolutions, they are not immediately comparable due to
their different sampling density. Several geostatistical techniques,
including indicator cokriging and collocated cokriging, can be used to
integrate different types of data into a geostatistical model. However,
with increasing numbers of variables the inference of the crosscovariance
model required for cokriging can be demanding in terms of
effort and computational time. In this paper a Gaussian-based Bayesian
updating approach is applied to integrate airborne radiometric data and
ground-sampled geochemical soil data to maximize information
generated from the soil survey, enabling more accurate geological
interpretation for the exploration and development of natural resources.
The Bayesian updating technique decomposes the collocated estimate
into two models: prior and likelihood models. The prior model is built
from primary information and the likelihood model is built from
secondary information. The prior model is then updated with the
likelihood model to build the final model. The approach allows multiple
secondary variables to be simultaneously integrated into the mapping of
the primary variable. The Bayesian updating approach is demonstrated
using a case study from Northern Ireland. The geostatistical technique
was used to improve the resolution of soil geochemistry, at a density of
one sample per 2 km2, by integrating more closely measured airborne
geophysical data from the GSNI Tellus Survey, measured over a
footprint of 65 x 200 m. The directly measured geochemistry data were
considered as primary data and the airborne radiometric data were used
as secondary data. The approach produced more detailed updated maps
and in particular enhanced information on the mapped distributions of
zinc, copper, and lead. The enhanced delineation of an elongated
northwest/southeast trending zone in the updated maps strengthened
the potential for discovering stratabound base metal deposits
Correlations and scaling in one-dimensional heat conduction
We examine numerically the full spatio-temporal correlation functions for all
hydrodynamic quantities for the random collision model introduced recently. The
autocorrelation function of the heat current, through the Kubo formula, gives a
thermal conductivity exponent of 1/3 in agreement with the analytical
prediction and previous numerical work. Remarkably, this result depends
crucially on the choice of boundary conditions: for periodic boundary
conditions (as opposed to open boundary conditions with heat baths) the
exponent is approximately 1/2. This is expected to be a generic feature of
systems with singular transport coefficients. All primitive hydrodynamic
quantities scale with the dynamic critical exponent predicted analytically.Comment: 7 pages, 11 figure
Quantum Search with Two-atom Collisions in Cavity QED
We propose a scheme to implement two-qubit Grover's quantum search algorithm
using Cavity Quantum Electrodynamics. Circular Rydberg atoms are used as
quantum bits (qubits). They interact with the electromagnetic field of a
non-resonant cavity . The quantum gate dynamics is provided by a
cavity-assisted collision, robust against decoherence processes. We present the
detailed procedure and analyze the experimental feasibility.Comment: 4 pages, 2 figure
Extended quantum conditional entropy and quantum uncertainty inequalities
Quantum states can be subjected to classical measurements, whose
incompatibility, or uncertainty, can be quantified by a comparison of certain
entropies. There is a long history of such entropy inequalities between
position and momentum. Recently these inequalities have been generalized to the
tensor product of several Hilbert spaces and we show here how their derivations
can be shortened to a few lines and how they can be generalized. All the
recently derived uncertainty relations utilize the strong subadditivity (SSA)
theorem; our contribution relies on directly utilizing the proof technique of
the original derivation of SSA.Comment: 4 page
Kosterlitz-Thouless Transition Line for the Two Dimensional Coulomb Gas
With a rigorous renormalization group approach, we study the pressure of the
two dimensional Coulomb Gas along a small piece of the Kosterlitz-Thouless
transition line, i.e. the boundary of the dipole region in the
activity-temperature phase-space.Comment: 61 pages, 2 figure
Life after charge noise: recent results with transmon qubits
We review the main theoretical and experimental results for the transmon, a
superconducting charge qubit derived from the Cooper pair box. The increased
ratio of the Josephson to charging energy results in an exponential suppression
of the transmon's sensitivity to 1/f charge noise. This has been observed
experimentally and yields homogeneous broadening, negligible pure dephasing,
and long coherence times of up to 3 microseconds. Anharmonicity of the energy
spectrum is required for qubit operation, and has been proven to be sufficient
in transmon devices. Transmons have been implemented in a wide array of
experiments, demonstrating consistent and reproducible results in very good
agreement with theory.Comment: 6 pages, 4 figures. Review article, accepted for publication in
Quantum Inf. Pro
On the universality of anomalous one-dimensional heat conductivity
In one and two dimensions, transport coefficients may diverge in the
thermodynamic limit due to long--time correlation of the corresponding
currents. The effective asymptotic behaviour is addressed with reference to the
problem of heat transport in 1d crystals, modeled by chains of classical
nonlinear oscillators. Extensive accurate equilibrium and nonequilibrium
numerical simulations confirm that the finite-size thermal conductivity
diverges with the system size as . However, the
exponent deviates systematically from the theoretical prediction
proposed in a recent paper [O. Narayan, S. Ramaswamy, Phys. Rev.
Lett. {\bf 89}, 200601 (2002)].Comment: 4 pages, submitted to Phys.Rev.
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