2,575 research outputs found
An equality between entanglement and uncertainty
Heisenberg's uncertainty principle implies that if one party (Alice) prepares
a system and randomly measures one of two incompatible observables, then
another party (Bob) cannot perfectly predict the measurement outcomes. This
implication assumes that Bob does not possess an additional system that is
entangled to the measured one; indeed the seminal paper of Einstein, Podolsky
and Rosen (EPR) showed that maximal entanglement allows Bob to perfectly win
this guessing game. Although not in contradiction, the observations made by EPR
and Heisenberg illustrate two extreme cases of the interplay between
entanglement and uncertainty. On the one hand, no entanglement means that Bob's
predictions must display some uncertainty. Yet on the other hand, maximal
entanglement means that there is no more uncertainty at all. Here we follow an
operational approach and give an exact relation - an equality - between the
amount of uncertainty as measured by the guessing probability, and the amount
of entanglement as measured by the recoverable entanglement fidelity. From this
equality we deduce a simple criterion for witnessing bipartite entanglement and
a novel entanglement monogamy equality.Comment: v2: published as "Entanglement-assisted guessing of complementary
measurement outcomes", 11 pages, 1 figur
Quantile-based bias correction and uncertainty quantification of extreme event attribution statements
Extreme event attribution characterizes how anthropogenic climate change may
have influenced the probability and magnitude of selected individual extreme
weather and climate events. Attribution statements often involve quantification
of the fraction of attributable risk (FAR) or the risk ratio (RR) and
associated confidence intervals. Many such analyses use climate model output to
characterize extreme event behavior with and without anthropogenic influence.
However, such climate models may have biases in their representation of extreme
events. To account for discrepancies in the probabilities of extreme events
between observational datasets and model datasets, we demonstrate an
appropriate rescaling of the model output based on the quantiles of the
datasets to estimate an adjusted risk ratio. Our methodology accounts for
various components of uncertainty in estimation of the risk ratio. In
particular, we present an approach to construct a one-sided confidence interval
on the lower bound of the risk ratio when the estimated risk ratio is infinity.
We demonstrate the methodology using the summer 2011 central US heatwave and
output from the Community Earth System Model. In this example, we find that the
lower bound of the risk ratio is relatively insensitive to the magnitude and
probability of the actual event.Comment: 28 pages, 4 figures, 3 table
Quantum preparation uncertainty and lack of information
The quantum uncertainty principle famously predicts that there exist
measurements that are inherently incompatible, in the sense that their outcomes
cannot be predicted simultaneously. In contrast, no such uncertainty exists in
the classical domain, where all uncertainty results from ignorance about the
exact state of the physical system. Here, we critically examine the concept of
preparation uncertainty and ask whether similarly in the quantum regime, some
of the uncertainty that we observe can actually also be understood as a lack of
information (LOI), albeit a lack of quantum information. We answer this
question affirmatively by showing that for the well known measurements employed
in BB84 quantum key distribution, the amount of uncertainty can indeed be
related to the amount of available information about additional registers
determining the choice of the measurement. We proceed to show that also for
other measurements the amount of uncertainty is in part connected to a LOI.
Finally, we discuss the conceptual implications of our observation to the
security of cryptographic protocols that make use of BB84 states.Comment: 7+15 pages, 4 figures. v2: expanded "Discussion" section, "Methods"
section moved before "Results" section, published versio
Quantifying statistical uncertainty in the attribution of human influence on severe weather
Event attribution in the context of climate change seeks to understand the
role of anthropogenic greenhouse gas emissions on extreme weather events,
either specific events or classes of events. A common approach to event
attribution uses climate model output under factual (real-world) and
counterfactual (world that might have been without anthropogenic greenhouse gas
emissions) scenarios to estimate the probabilities of the event of interest
under the two scenarios. Event attribution is then quantified by the ratio of
the two probabilities. While this approach has been applied many times in the
last 15 years, the statistical techniques used to estimate the risk ratio based
on climate model ensembles have not drawn on the full set of methods available
in the statistical literature and have in some cases used and interpreted the
bootstrap method in non-standard ways. We present a precise frequentist
statistical framework for quantifying the effect of sampling uncertainty on
estimation of the risk ratio, propose the use of statistical methods that are
new to event attribution, and evaluate a variety of methods using statistical
simulations. We conclude that existing statistical methods not yet in use for
event attribution have several advantages over the widely-used bootstrap,
including better statistical performance in repeated samples and robustness to
small estimated probabilities. Software for using the methods is available
through the climextRemes package available for R or Python. While we focus on
frequentist statistical methods, Bayesian methods are likely to be particularly
useful when considering sources of uncertainty beyond sampling uncertainty.Comment: 41 pages, 11 figures, 1 tabl
A time-dependent Tsirelson's bound from limits on the rate of information gain in quantum systems
We consider the problem of distinguishing between a set of arbitrary quantum
states in a setting in which the time available to perform the measurement is
limited. We provide simple upper bounds on how well we can perform state
discrimination in a given time as a function of either the average energy or
the range of energies available during the measurement. We exhibit a specific
strategy that nearly attains this bound. Finally, we consider several
applications of our result. First, we obtain a time-dependent Tsirelson's bound
that limits the extent of the Bell inequality violation that can be in
principle be demonstrated in a given time t. Second, we obtain a
Margolus-Levitin type bound when considering the special case of distinguishing
orthogonal pure states.Comment: 15 pages, revtex, 1 figur
UCD Candidates in the Hydra Cluster
NGC 3311, the giant cD galaxy in the Hydra cluster (A1060), has one of the
largest globular cluster systems known. We describe new Gemini GMOS (g',i')
photometry of the NGC 3311 field which reveals that the red, metal-rich side of
its globular cluster population extends smoothly upward into the mass range
associated with the new class of Ultra-Compact Dwarfs (UCDs). We identify 29
UCD candidates with estimated masses > 6x10^6 solar masses and discuss their
characteristics. This UCD-like sequence is the most well defined one yet seen,
and reinforces current ideas that the high-mass end of the globular cluster
sequence merges continuously into the UCD sequence, which connects in turn to
the E galaxy structural sequence.Comment: 5 pages, 3 figures. Accepted for publication in ApJ Letter
VALIDATION, OPTIMIZATION, AND IMAGE PROCESSING OF SPIRAL CINE DENSE MAGNETIC RESONANCE IMAGING FOR THE QUANTIFICATION OF LEFT AND RIGHT VENTRICULAR MECHANICS
Recent evidence suggests that cardiac mechanics (e.g. cardiac strains) are better measures of heart function compared to common clinical metrics like ejection fraction. However, commonly-used parameters of cardiac mechanics remain limited to just a few measurements averaged over the whole left ventricle. We hypothesized that recent advances in cardiac magnetic resonance imaging (MRI) could be extended to provide measures of cardiac mechanics throughout the left and right ventricles (LV and RV, respectively).
Displacement Encoding with Stimulated Echoes (DENSE) is a cardiac MRI technique that has been validated for measuring LV mechanics at a magnetic field strength of 1.5 T but not at higher field strengths such as 3.0 T. However, it is desirable to perform DENSE at 3.0 T, which would yield a better signal to noise ratio for imaging the thin RV wall. Results in Chapter 2 support the hypothesis that DENSE has similar accuracy at 1.5 and 3.0 T.
Compared to standard, clinical cardiac MRI, DENSE requires more expertise to perform and is not as widely used. If accurate mechanics could be measured from standard MRI, the need for DENSE would be reduced. However, results from Chapter 3 support the hypothesis that measured cardiac mechanics from standard MRI do not agree with, and thus cannot be used in place of, measurements from DENSE.
Imaging the thin RV wall with its complex contraction pattern requires both three-dimensional (3D) measures of myocardial motion and higher resolution imaging. Results from Chapter 4 support the hypothesis that a lower displacement-encoding frequency can be used to allow for easier processing of 3D DENSE images. Results from Chapter 5 support the hypothesis that images with higher resolution (decreased blurring) can be achieved by using more spiral interleaves during the DENSE image acquisition.
Finally, processing DENSE images to yield measures of cardiac mechanics in the LV is relatively simple due to the LV’s mostly cylindrical geometry. Results from Chapter 6 support the hypothesis that a local coordinate system can be adapted to the geometry of the RV to quantify mechanics in an equivalent manner as the LV.
In summary, cardiac mechanics can now be quantified throughout the left and right ventricles using DENSE cardiac MRI
Multi-qubit Randomized Benchmarking Using Few Samples
Randomized benchmarking (RB) is an efficient and robust method to
characterize gate errors in quantum circuits. Averaging over random sequences
of gates leads to estimates of gate errors in terms of the average fidelity.
These estimates are isolated from the state preparation and measurement errors
that plague other methods like channel tomography and direct fidelity
estimation. A decisive factor in the feasibility of randomized benchmarking is
the number of sampled sequences required to obtain rigorous confidence
intervals. Previous bounds were either prohibitively loose or required the
number of sampled sequences to scale exponentially with the number of qubits in
order to obtain a fixed confidence interval at a fixed error rate. Here we show
that, with a small adaptation to the randomized benchmarking procedure, the
number of sampled sequences required for a fixed confidence interval is
dramatically smaller than could previously be justified. In particular, we show
that the number of sampled sequences required is essentially independent of the
number of qubits and scales favorably with the average error rate of the system
under investigation. We also show that the number of samples required for long
sequence lengths can be made substantially smaller than previous rigorous
results (even for single qubits) as long as the noise process under
investigation is not unitary. Our results bring rigorous randomized
benchmarking on systems with many qubits into the realm of experimental
feasibility.Comment: v3: Added discussion of the impact of variance heteroskedasticity on
the RB fitting procedure. Close to published versio
A strong converse for classical channel coding using entangled inputs
A fully general strong converse for channel coding states that when the rate
of sending classical information exceeds the capacity of a quantum channel, the
probability of correctly decoding goes to zero exponentially in the number of
channel uses, even when we allow code states which are entangled across several
uses of the channel. Such a statement was previously only known for classical
channels and the quantum identity channel. By relating the problem to the
additivity of minimum output entropies, we show that a strong converse holds
for a large class of channels, including all unital qubit channels, the
d-dimensional depolarizing channel and the Werner-Holevo channel. This further
justifies the interpretation of the classical capacity as a sharp threshold for
information-transmission.Comment: 9 pages, revte
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