2,062 research outputs found
Distinguishability times and asymmetry monotone-based quantum speed limits in the Bloch ball
For both unitary and open qubit dynamics, we compare asymmetry monotone-based
bounds on the minimal time required for an initial qubit state to evolve to a
final qubit state from which it is probabilistically distinguishable with fixed
minimal error probability (i.e., the minimal error distinguishability time).
For the case of unitary dynamics generated by a time-independent Hamiltonian,
we derive a necessary and sufficient condition on two asymmetry monotones that
guarantees that an arbitrary state of a two-level quantum system or a separable
state of two-level quantum systems will unitarily evolve to another state
from which it can be distinguished with a fixed minimal error probability
. This condition is used to order the set of qubit states
based on their distinguishability time, and to derive an optimal release time
for driven two-level systems such as those that occur, e.g., in the
Landau-Zener problem. For the case of non-unitary dynamics, we compare three
lower bounds to the distinguishability time, including a new type of lower
bound which is formulated in terms of the asymmetry of the uniformly
time-twirled initial system-plus-environment state with respect to the
generator of the Stinespring isometry corresponding to the dynamics,
specifically, in terms of ,
where .Comment: 13 pages, 4 figure
On Estimation of the Post-Newtonian Parameters in the Gravitational-Wave Emission of a Coalescing Binary
The effect of the recently obtained 2nd post-Newtonian corrections on the
accuracy of estimation of parameters of the gravitational-wave signal from a
coalescing binary is investigated. It is shown that addition of this correction
degrades considerably the accuracy of determination of individual masses of the
members of the binary. However the chirp mass and the time parameter in the
signal is still determined to a very good accuracy. The possibility of
estimation of effects of other theories of gravity is investigated. The
performance of the Newtonian filter is investigated and it is compared with
performance of post-Newtonian search templates introduced recently. It is shown
that both search templates can extract accurately useful information about the
binary.Comment: 34 pages, 118Kb, LATEX format, submitted to Phys. Rev.
Effect of Photometric Redshift Uncertainties on Weak Lensing Tomography
We perform a systematic analysis of the effects of photometric redshift
uncertainties on weak lensing tomography. We describe the photo-z distribution
with a bias and Gaussian scatter that are allowed to vary arbitrarily between
intervals of dz = 0.1 in redshift.While the mere presence of bias and scatter
does not substantially degrade dark energy information, uncertainties in both
parameters do. For a fiducial next-generation survey each would need to be
known to better than about 0.003-0.01 in redshift for each interval in order to
lead to less than a factor of 1.5 increase in the dark energy parameter errors.
The more stringent requirement corresponds to a larger dark energy parameter
space, when redshift variation in the equation of state of dark energy is
allowed.Of order 10^4-10^5 galaxies with spectroscopic redshifts fairly sampled
from the source galaxy distribution will be needed to achieve this level of
calibration. If the sample is composed of multiple galaxy types, a fair sample
would be required for each. These requirements increase in stringency for more
ambitious surveys; we quantify such scalings with a convenient fitting formula.
No single aspect of a photometrically binned selection of galaxies such as
their mean or median suffices, indicating that dark energy parameter
determinations are sensitive to the shape and nature of outliers in the photo-z
redshift distribution.Comment: 10 pages, 12 figures, accepted by Ap
Information geometry of Gaussian channels
We define a local Riemannian metric tensor in the manifold of Gaussian
channels and the distance that it induces. We adopt an information-geometric
approach and define a metric derived from the Bures-Fisher metric for quantum
states. The resulting metric inherits several desirable properties from the
Bures-Fisher metric and is operationally motivated from distinguishability
considerations: It serves as an upper bound to the attainable quantum Fisher
information for the channel parameters using Gaussian states, under generic
constraints on the physically available resources. Our approach naturally
includes the use of entangled Gaussian probe states. We prove that the metric
enjoys some desirable properties like stability and covariance. As a byproduct,
we also obtain some general results in Gaussian channel estimation that are the
continuous-variable analogs of previously known results in finite dimensions.
We prove that optimal probe states are always pure and bounded in the number of
ancillary modes, even in the presence of constraints on the reduced state input
in the channel. This has experimental and computational implications: It limits
the complexity of optimal experimental setups for channel estimation and
reduces the computational requirements for the evaluation of the metric:
Indeed, we construct a converging algorithm for its computation. We provide
explicit formulae for computing the multiparametric quantum Fisher information
for dissipative channels probed with arbitrary Gaussian states, and provide the
optimal observables for the estimation of the channel parameters (e.g. bath
couplings, squeezing, and temperature).Comment: 19 pages, 4 figure
Constraining reionization using 21 cm observations in combination with CMB and Lyman-alpha forest data
In this paper, we explore the constraints on the reionization history that
are provided by current observations of the Lyman-alpha forest and the CMB.
Rather than using a particular semi-analytic model, we take the novel approach
of parametrizing the ionizing sources with arbitrary functions, and perform
likelihood analyses to constrain possible reionization histories. We find model
independent conclusions that reionization is likely to be mostly complete by
z=8 and that the IGM was 50% ionized at z=9-10. Upcoming low-frequency
observations of the redshifted 21 cm line of neutral hydrogen are expected to
place significantly better constraints on the hydrogen neutral fraction at
6<z<12. We use our constraints on the reionization history to predict the
likely amplitude of the 21 cm power spectrum and show that observations with
the highest signal-to-noise ratio will most likely be made at frequencies
corresponding to z=9-10. This result provides an important guide to the
upcoming 21 cm observations. Finally, we assess the impact that measurement of
the neutral fraction will have on our knowledge of reionization and the early
source population. Our results show that a single measurement of the neutral
fraction mid-way through the reionization era will significantly enhance our
knowledge of the entire reionization history.Comment: 15 pages, 16 figures, submitted to MNRA
On a generalized entropic uncertainty relation in the case of the qubit
We revisit generalized entropic formulations of the uncertainty principle for
an arbitrary pair of quantum observables in two-dimensional Hilbert space.
R\'enyi entropy is used as uncertainty measure associated with the distribution
probabilities corresponding to the outcomes of the observables. We derive a
general expression for the tight lower bound of the sum of R\'enyi entropies
for any couple of (positive) entropic indices (\alpha,\beta). Thus, we have
overcome the H\"older conjugacy constraint imposed on the entropic indices by
Riesz-Thorin theorem. In addition, we present an analytical expression for the
tight bound inside the square [0 , 1/2] x [0 , 1/2] in the \alpha-\beta plane,
and a semi-analytical expression on the line \beta = \alpha. It is seen that
previous results are included as particular cases. Moreover, we present an
analytical but suboptimal bound for any couple of indices. In all cases, we
provide the minimizing states.Comment: 15 pages, 6 figure
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