8,192 research outputs found

    Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels

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    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

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    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

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    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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