It is well known that a suggestive connection links Schr?dinger’s equation (SE) and the information-optimizing principle based on Fisher’s information measure (FIM). It has been shown that this entails the existence...It is well known that a suggestive connection links Schr?dinger’s equation (SE) and the information-optimizing principle based on Fisher’s information measure (FIM). It has been shown that this entails the existence of a Legendre transform structure underlying the SE. Such a structure leads to a first order partial differential equation (PDE) for the SE’s eigenvalues from which a complete solution for them can be obtained. We test this theory with regards to anharmonic oscillators (AHO). AHO pose a long-standing problem and received intense attention motivated by problems in quantum field theory and molecular physics. By appeal to the Cramer Rao bound we are able to Fisher-infer the energy eigenvalues without explicitly solving Schr?dinger’s equation. Remarkably enough, and in contrast with standard variational approaches, our present procedure does not involve free fitting parameters.展开更多
The enhancement of the precision of phase estimation in quantum metrology is investigated by employing weak measurement （WM） and quantum measurement reversal （QMR）. We derive the exact expressions of the optimal q...The enhancement of the precision of phase estimation in quantum metrology is investigated by employing weak measurement （WM） and quantum measurement reversal （QMR）. We derive the exact expressions of the optimal quantum Fisher information （QFI） and success probability of phase estimation for an exactly solving model consisting of a qubit interacting with a structured reservoir. We show that the QFI can be obviously enhanced by means of the WM and QMR in different regimes. In addition, we also show that the magnitude of the decoherence involved in the WM and QMR can be a general complex number, which extends the applicable scope of the WM and QMR approach.展开更多
近年来,量化开放量子系统中的非马尔科夫效应已经成为了量子消相干控制领域研究中的一个重要科学问题.本文对于单个开放的两能级系统,将基于量子Fisher信息的非马尔科夫度量从系统初态为纯态的情况推广到系统初态为任意态的情况.作为该...近年来,量化开放量子系统中的非马尔科夫效应已经成为了量子消相干控制领域研究中的一个重要科学问题.本文对于单个开放的两能级系统,将基于量子Fisher信息的非马尔科夫度量从系统初态为纯态的情况推广到系统初态为任意态的情况.作为该非马尔科夫度量的应用,分别研究了利用量子Fisher信息在检测一个两能级系统受到零温度振幅耗散通道、相位衰减通道和随机幺正通道作用时对应非马尔可夫过程发生满足的条件.研究结果显示:一个相位参数的量子Fisher信息对这三种衰减通道的非马尔科夫过程发生所满足的条件与系统初态的选择是无关的.进一步,对于振幅耗散通道和相位衰减通道,非马尔科夫过程发生的条件同基于迹距离、映射的可分性、量子互信息和量子Fisher信息矩阵等给出的条件是等价的.如预期的一样,对于振幅耗散通道情况且选择系统初态为最优化纯态时,相应的结果正是Lu等获得的结果(Lu X M,Wang X G,Sun C P 2010 Phys.Rev.A 82042103);而对于随机幺正通道,其马尔可夫过程发生的条件同基于迹距离、映射的可分性、量子互信息和量子Fisher信息矩阵等给出的条件是不完全等价的.另外,得到了一个有趣的关系:在这三种耗散通道模型中系统演化态的量子l范数相干性的平方正好等于相位参数的量子Fisher信息.总之,本文得到的结果不仅完善了用量子Fisher信息来检测开放系统中非马尔科夫效应的应用范围,同时也进一步彰显了量子Fisher信息在量子信息处理中独特的作用.展开更多
文摘It is well known that a suggestive connection links Schr?dinger’s equation (SE) and the information-optimizing principle based on Fisher’s information measure (FIM). It has been shown that this entails the existence of a Legendre transform structure underlying the SE. Such a structure leads to a first order partial differential equation (PDE) for the SE’s eigenvalues from which a complete solution for them can be obtained. We test this theory with regards to anharmonic oscillators (AHO). AHO pose a long-standing problem and received intense attention motivated by problems in quantum field theory and molecular physics. By appeal to the Cramer Rao bound we are able to Fisher-infer the energy eigenvalues without explicitly solving Schr?dinger’s equation. Remarkably enough, and in contrast with standard variational approaches, our present procedure does not involve free fitting parameters.
基金supported by the National Natural Science Foundation of China(Grants No.11247294)the Research Foundation of Education Bureau of Hunan Province,China(Grant No.12C0826)+2 种基金the Doctor Foundation Startup from Hunan University of Arts and Science,China(Grant No.13101039)the Key Laboratory of Photoelectricity Information Integration and Optics Manufacture Technology in Hunan Province,Chinathe Construct Program of the Key Discipline in Hunan University of Arts and Science(Optics),China
文摘The enhancement of the precision of phase estimation in quantum metrology is investigated by employing weak measurement （WM） and quantum measurement reversal （QMR）. We derive the exact expressions of the optimal quantum Fisher information （QFI） and success probability of phase estimation for an exactly solving model consisting of a qubit interacting with a structured reservoir. We show that the QFI can be obviously enhanced by means of the WM and QMR in different regimes. In addition, we also show that the magnitude of the decoherence involved in the WM and QMR can be a general complex number, which extends the applicable scope of the WM and QMR approach.
文摘近年来,量化开放量子系统中的非马尔科夫效应已经成为了量子消相干控制领域研究中的一个重要科学问题.本文对于单个开放的两能级系统,将基于量子Fisher信息的非马尔科夫度量从系统初态为纯态的情况推广到系统初态为任意态的情况.作为该非马尔科夫度量的应用,分别研究了利用量子Fisher信息在检测一个两能级系统受到零温度振幅耗散通道、相位衰减通道和随机幺正通道作用时对应非马尔可夫过程发生满足的条件.研究结果显示:一个相位参数的量子Fisher信息对这三种衰减通道的非马尔科夫过程发生所满足的条件与系统初态的选择是无关的.进一步,对于振幅耗散通道和相位衰减通道,非马尔科夫过程发生的条件同基于迹距离、映射的可分性、量子互信息和量子Fisher信息矩阵等给出的条件是等价的.如预期的一样,对于振幅耗散通道情况且选择系统初态为最优化纯态时,相应的结果正是Lu等获得的结果(Lu X M,Wang X G,Sun C P 2010 Phys.Rev.A 82042103);而对于随机幺正通道,其马尔可夫过程发生的条件同基于迹距离、映射的可分性、量子互信息和量子Fisher信息矩阵等给出的条件是不完全等价的.另外,得到了一个有趣的关系:在这三种耗散通道模型中系统演化态的量子l范数相干性的平方正好等于相位参数的量子Fisher信息.总之,本文得到的结果不仅完善了用量子Fisher信息来检测开放系统中非马尔科夫效应的应用范围,同时也进一步彰显了量子Fisher信息在量子信息处理中独特的作用.
