Holevo bound plays an important role in quantum metrology as it sets the ultimate limit for multi-parameter estimations,which can be asymptotically achieved.Except for some trivial cases,the Holevo bound is implicitly...Holevo bound plays an important role in quantum metrology as it sets the ultimate limit for multi-parameter estimations,which can be asymptotically achieved.Except for some trivial cases,the Holevo bound is implicitly defined and formulated with the help of weight matrices.Here we report the first instance of an intrinsic Holevo bound,namely,without any reference to weight matrices,in a nontrivial case.Specifically,we prove that the Holevo bound for estimating two parameters of a qubit is equivalent to the joint constraint imposed by two quantum Cramér–Rao bounds corresponding to symmetric and right logarithmic derivatives.This weightless form of Holevo bound enables us to determine the precise range of independent entries of the mean-square error matrix,i.e.,two variances and one covariance that quantify the precisions of the estimation,as illustrated by different estimation models.Our result sheds some new light on the relations between the Holevo bound and quantum Cramer–Rao bounds.Possible generalizations are discussed.展开更多
The Holevo capacity of a generalized amplitude-damping channel is investigated by using a numerical method. It is shown that the Holevo capacity depends on the channel parameters representing the ambient temperature a...The Holevo capacity of a generalized amplitude-damping channel is investigated by using a numerical method. It is shown that the Holevo capacity depends on the channel parameters representing the ambient temperature and fidelity. In particular, under a special condition, the Holevo capacity of the generalized amplitude-damping channel can be written as an analytical expression.展开更多
We prove a new version of the Holevo bound employing the Hilbert-Schmidt norm instead of the Kullback-Leibler divergence. Suppose Alice is sending classical information to Bob by using a quantum channel while Bob is p...We prove a new version of the Holevo bound employing the Hilbert-Schmidt norm instead of the Kullback-Leibler divergence. Suppose Alice is sending classical information to Bob by using a quantum channel while Bob is performing some projective measurements. We bound the classical mutual information in terms of the Hilbert-Schmidt norm by its quantum Hilbert-Schmidt counterpart. This constitutes a Holevo-type upper bound on the classical information transmission rate via a quantum channel. The resulting inequality is rather natural and intuitive relating classical and quantum expressions using the same measure.展开更多
In this paper, we characterize the saturation of four universal inequalities in quantum information theory, including a variant version of strong subadditivity inequality for von Neumann entropy, the coherent informat...In this paper, we characterize the saturation of four universal inequalities in quantum information theory, including a variant version of strong subadditivity inequality for von Neumann entropy, the coherent information inequality, the Holevo quantity, and average entropy inequalities. These results shed new light on quantum information inequalities.展开更多
We use Hypergeometric Gaussian-II(HyGG-II)modes to investigate the impacts of non-Kolmogorov atmospheric turbulence on the Holevo channel capacity of a quantum communication scheme.The capacity of HyGG-II modes can be...We use Hypergeometric Gaussian-II(HyGG-II)modes to investigate the impacts of non-Kolmogorov atmospheric turbulence on the Holevo channel capacity of a quantum communication scheme.The capacity of HyGG-II modes can be higher than that of Laguerre-Gaussian modes via modulating the hollowness parameter.The influences of low-order turbulence aberrations including tilt,defocus,astigmatism,and coma on the capacity are also explored.Generally,tilt aberration dominates among all low-order aberrations and defocus and astigmatism aberrations are always negligible.By contrast,the effect of coma aberration can be enhanced to be non-negligible when the turbulence strength or the channel zenith angle is enhanced.We also show that only the total and tilt aberrations are sensitive to the non-Kolmogorov power-law exponent.Our results may contribute to the quantum optical communication as well as aberration compensation in turbulent channels utilizing the novel family of vortex beams.展开更多
基金Project supported by the Key-Area Research and Development Program of Guangdong Province of China(Grant Nos.2020B0303010001 and SIQSE202104).
文摘Holevo bound plays an important role in quantum metrology as it sets the ultimate limit for multi-parameter estimations,which can be asymptotically achieved.Except for some trivial cases,the Holevo bound is implicitly defined and formulated with the help of weight matrices.Here we report the first instance of an intrinsic Holevo bound,namely,without any reference to weight matrices,in a nontrivial case.Specifically,we prove that the Holevo bound for estimating two parameters of a qubit is equivalent to the joint constraint imposed by two quantum Cramér–Rao bounds corresponding to symmetric and right logarithmic derivatives.This weightless form of Holevo bound enables us to determine the precise range of independent entries of the mean-square error matrix,i.e.,two variances and one covariance that quantify the precisions of the estimation,as illustrated by different estimation models.Our result sheds some new light on the relations between the Holevo bound and quantum Cramer–Rao bounds.Possible generalizations are discussed.
基金Project supported by the National Natural Science Foundation of China （Grant No 10374025）, and the Natural Science Foundation of Hunan Normal University, China （Grant No 22040640）.
文摘The Holevo capacity of a generalized amplitude-damping channel is investigated by using a numerical method. It is shown that the Holevo capacity depends on the channel parameters representing the ambient temperature and fidelity. In particular, under a special condition, the Holevo capacity of the generalized amplitude-damping channel can be written as an analytical expression.
文摘We prove a new version of the Holevo bound employing the Hilbert-Schmidt norm instead of the Kullback-Leibler divergence. Suppose Alice is sending classical information to Bob by using a quantum channel while Bob is performing some projective measurements. We bound the classical mutual information in terms of the Hilbert-Schmidt norm by its quantum Hilbert-Schmidt counterpart. This constitutes a Holevo-type upper bound on the classical information transmission rate via a quantum channel. The resulting inequality is rather natural and intuitive relating classical and quantum expressions using the same measure.
基金Supported by National Natural Science Foundation of China under Grant Nos.11301124,11171301the Doctoral Programs Foundation of Ministry of Education of China under Grant No.J20130061
文摘In this paper, we characterize the saturation of four universal inequalities in quantum information theory, including a variant version of strong subadditivity inequality for von Neumann entropy, the coherent information inequality, the Holevo quantity, and average entropy inequalities. These results shed new light on quantum information inequalities.
基金Project supported by the National Key Research and Development Program of China(Grant No.2022YFE0122300)the National Natural Science Foundation of China(Grant Nos.61871202 and 11811530052)
文摘We use Hypergeometric Gaussian-II(HyGG-II)modes to investigate the impacts of non-Kolmogorov atmospheric turbulence on the Holevo channel capacity of a quantum communication scheme.The capacity of HyGG-II modes can be higher than that of Laguerre-Gaussian modes via modulating the hollowness parameter.The influences of low-order turbulence aberrations including tilt,defocus,astigmatism,and coma on the capacity are also explored.Generally,tilt aberration dominates among all low-order aberrations and defocus and astigmatism aberrations are always negligible.By contrast,the effect of coma aberration can be enhanced to be non-negligible when the turbulence strength or the channel zenith angle is enhanced.We also show that only the total and tilt aberrations are sensitive to the non-Kolmogorov power-law exponent.Our results may contribute to the quantum optical communication as well as aberration compensation in turbulent channels utilizing the novel family of vortex beams.
