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A New Approach to Cramér-Rao Bounds for Quantum State Estimation

Hiroshi Nagaoka

WORLD SCIENTIFIC eBooksFeb 1, 200540 citations

Two kinds of asymptotic bounds in quantum channel estimation

Masahito Hayashi

In order to treat the covariant approach and the Cramer-Rao approach in a unified viewpoint, we compare the Cramer-Rao bound and the local asymptotic mini-max bound, which coincides the limit of Bayesian bound in the group covariant case. it is shown that the local asymptotic mini-max bound is strictly larger than the Cramer-Rao bound in the phase estimation case while the both bounds coincide when the minimum mean square error decreases with the order O(1/n). We also derive a sufficient condition for that the minimum mean square error decreases with the order O(1/n).In order to treat the covariant approach and the Cramer-Rao approach in a unified viewpoint, we compare the Cramer-Rao bound and the local asymptotic mini-max bound, which coincides the limit of Bayesian bound in the group covariant case. it is shown that the local asymptotic mini-max bound is strictly larger than the Cramer-Rao bound in the phase estimation case while the both bounds coincide when the minimum mean square error decreases with the order O(1/n). We also derive a sufficient condition for that the minimum mean square error decreases with the order O(1/n).

Mar 24, 20101 citation

Cramer-Rao lower bound of channel estimator in continuous variable quantum key distribution

YoungJun Kim, Young‐Chai Ko

The channel estimation is one of the essential components to make the long distance transmission of continuous variable quantum key distribution (CV-QKD). In this paper we provide the Cramer-Rao lower bound (CRLB) of the channel estimator, which is the minimum variance that an estimator can achieve. We compare CRLB with the channel transmission parameter estimator proposed in [15] for long distance CV-QKD systems.

International Conference on Information and Communication Technology Convergence (ICTC)Oct 1, 20161 citation

STATISTICAL ESTIMATION OF A QUANTUM CHANNEL

Akio Fujiwara

Foundations of Quantum Mechanics in the Light of New TechnologyOct 1, 20020 citations

Comparison of estimation limits for quantum two-parameter estimation

Simon K. Yung, Lorcán O. Conlon, Jie Zhao +2 more

Measurement estimation bounds for local quantum multiparameter estimation, which provide lower bounds on possible measurement uncertainties, have so far been formulated in two ways: by extending the classical Cramér-Rao bound (e.g., the quantum Cramér-Rao bound and the Nagaoka Cramér-Rao bound) and by incorporating the parameter estimation framework with the uncertainty principle, as in the Lu-Wang uncertainty relation. In this work, we present a general framework that allows a direct comparison between these different types of estimation limits. Specifically, we compare the attainability of the Nagaoka Cramér-Rao bound and the Lu-Wang uncertainty relation, using analytical and numerical techniques. We show that these two limits can provide different information about the physically attainable precision. We present an example where both limits provide the same attainable precision and an example where the Lu-Wang uncertainty relation is not attainable even for pure states. We further demonstrate that the unattainability in the latter case arises because the figure of merit underpinning the Lu-Wang uncertainty relation (the difference between the quantum and classical Fisher information matrices) does not necessarily agree with the conventionally used figure of merit (mean-squared error). The results offer insights into the general attainability and applicability of the Lu-Wang uncertainty relation. Furthermore, our proposed framework for comparing bounds of different types may prove useful in other settings. Published by the American Physical Society 2024Measurement estimation bounds for local quantum multiparameter estimation, which provide lower bounds on possible measurement uncertainties, have so far been formulated in two ways: by extending the classical Cramér-Rao bound (e.g., the quantum Cramér-Rao bound and the Nagaoka Cramér-Rao bound) and by incorporating the parameter estimation framework with the uncertainty principle, as in the Lu-Wang uncertainty relation. In this work, we present a general framework that allows a direct comparison between these different types of estimation limits. Specifically, we compare the attainability of the Nagaoka Cramér-Rao bound and the Lu-Wang uncertainty relation, using analytical and numerical techniques. We show that these two limits can provide different information about the physically attainable precision. We present an example where both limits provide the same attainable precision and an example where the Lu-Wang uncertainty relation is not attainable even for pure states. We further demonstrate that the unattainability in the latter case arises because the figure of merit underpinning the Lu-Wang uncertainty relation (the difference between the quantum and classical Fisher information matrices) does not necessarily agree with the conventionally used figure of merit (mean-squared error). The results offer insights into the general attainability and applicability of the Lu-Wang uncertainty relation. Furthermore, our proposed framework for comparing bounds of different types may prove useful in other settings. Published by the American Physical Society 2024

arXiv:2407.12466Physical Review ResearchSep 18, 20246 citations

ENTANGLEMENT-ASSISTED ESTIMATION OF QUANTUM CHANNELS

Akio Fujiwara

Foundations of Quantum Mechanics in the Light of New TechnologyJun 1, 20060 citations

Comparison Between the Cramer-Rao and the Mini-max Approaches in Quantum Channel Estimation

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