8,192 research outputs found
Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels
We present a comprehensive analysis of the performance of different classes
of Gaussian states in the estimation of Gaussian phase-insensitive dissipative
channels. In particular, we investigate the optimal estimation of the damping
constant and reservoir temperature. We show that, for two-mode squeezed vacuum
probe states, the quantum-limited accuracy of both parameters can be achieved
simultaneously. Moreover, we show that for both parameters two-mode squeezed
vacuum states are more efficient than either coherent, thermal or single-mode
squeezed states. This suggests that at high energy regimes two-mode squeezed
vacuum states are optimal within the Gaussian setup. This optimality result
indicates a stronger form of compatibility for the estimation of the two
parameters. Indeed, not only the minimum variance can be achieved at fixed
probe states, but also the optimal state is common to both parameters.
Additionally, we explore numerically the performance of non-Gaussian states for
particular parameter values to find that maximally entangled states within
D-dimensional cutoff subspaces perform better than any randomly sampled states
with similar energy. However, we also find that states with very similar
performance and energy exist with much less entanglement than the maximally
entangled ones.Comment: 14 pages, 6 figure
Improving Frequency Estimation under Local Differential Privacy
Local Differential Privacy protocols are stochastic protocols used in data
aggregation when individual users do not trust the data aggregator with their
private data. In such protocols there is a fundamental tradeoff between user
privacy and aggregator utility. In the setting of frequency estimation,
established bounds on this tradeoff are either nonquantitative, or far from
what is known to be attainable. In this paper, we use information-theoretical
methods to significantly improve established bounds. We also show that the new
bounds are attainable for binary inputs. Furthermore, our methods lead to
improved frequency estimators, which we experimentally show to outperform
state-of-the-art methods
The Sensing Capacity of Sensor Networks
This paper demonstrates fundamental limits of sensor networks for detection
problems where the number of hypotheses is exponentially large. Such problems
characterize many important applications including detection and classification
of targets in a geographical area using a network of sensors, and detecting
complex substances with a chemical sensor array. We refer to such applications
as largescale detection problems. Using the insight that these problems share
fundamental similarities with the problem of communicating over a noisy
channel, we define a quantity called the sensing capacity and lower bound it
for a number of sensor network models. The sensing capacity expression differs
significantly from the channel capacity due to the fact that a fixed sensor
configuration encodes all states of the environment. As a result, codewords are
dependent and non-identically distributed. The sensing capacity provides a
bound on the minimal number of sensors required to detect the state of an
environment to within a desired accuracy. The results differ significantly from
classical detection theory, and provide an ntriguing connection between sensor
networks and communications. In addition, we discuss the insight that sensing
capacity provides for the problem of sensor selection.Comment: Submitted to IEEE Transactions on Information Theory, November 200
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