Uncertainty relations for noise and disturbance in generalized quantum measurements

Heisenberg’s uncertainty relation for measurement noise and disturbance is commonly understood to state that in any measurement the product of the position measurement noise and the momentum disturbance is not less than Planck’s constant divided by 4π. However, it has been shown in many ways that this relation holds only for a restricted class of measuring apparatuses in the most general formulation of measuring processes. Here, Heisenberg’s uncertainty relation is generalized to a relation that holds for all the possible quantum measurements, from which rigorous conditions are obtained for measuring apparatuses to satisfy Heisenberg’s relation. In particular, every apparatus with the noise and the disturbance statistically independent from the measured object is proven to satisfy Heisenberg’s relation. For this purpose, all the possible quantum measurements are characterized by naturally acceptable axioms. Then, a mathematical notion of the distance between probability operator valued measures and observables is introduced and the basic properties are explored. Based on this notion, the measurement noise and disturbance are naturally defined for any quantum measurements in a model independent formulation. Under this formulation, various relations for noise and disturbance are also derived for apparatuses with independent noise, independent disturbance, unbiased noise, and unbiased disturbance as well as noiseless apparatuses and nondisturbing apparatuses. Two models of position measurements are also discussed in the light of the new uncertainty relations to show that Heisenberg’s relation can be violated even by approximately repeatable position measurements.     

The Generalized Uncertainty Principle

The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit of the measurement precision of incompatible observables. Here it is shown that the traditional uncertainty relation in fact belongs to the leading order approximation of a generalized uncertainty relation. That is, the leading order linear dependence of observables gives the Heisenberg type of uncertainty relations, while higher order nonlinear dependence may reveal more different and interesting correlation properties. Applications of the generalized uncertainty relation and the high order nonlinear dependence between observables in quantum information science are also discussed.     

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根据垂直扫描干涉技术结合样品折射率与密度间的依赖关系,建立了低密度SiO2泡沫微球密度的检测方法,用Lorentz-Lorenz和Gladstone-Dale公式分析了SiO2泡沫微球折射率与密度间的依赖关系。实验结果和测量误差估计表明,利用垂直扫描干涉技术并结合Gladstone-Dale分析方法,可实现对低密度SiO2泡沫微球密度的精密检测,其测量误差好于5%。     

基于MATLAB的直线度测量不确定度评定程序设计

Keywords: Straightness ; uncertainty ; programming     

基于最优估计理论、联合星载主被动传感器资料的液态云微物理特性反演研究

针对液态云微物理特性精确反演的迫切需求, 综合主被动传感器的探测优势, 联合CloudSat雷达反射率和Aqua光学厚度资料, 提出基于最优估计理论的液态云微物理参数反演算法.通过假设粒子谱服从对数正态分布, 基于前向物理模式建立测量变量与反演变量的函数关系, 借助谱分布参数的先验信息、通过算法迭代得到谱参数的最优解, 进而利用前向物理模式反演液态云微物理参数, 并根据误差传递理论计算反演不确定度.通过设计反演方案, 基于实测个例数据并与CloudSat官方发布产品和经验算法反演结果对比验证.结果表明: 基于最优估计理论、联合主被动传感器资料的液态云微物理参数反演结果与官方发布产品一致性较好, 弥补了经验算法误差大、扩展性差的不足, 对于开展国内星载和机载W波段毫米波雷达液态云微物理参数反演研究具有重要的借鉴意义. 关键词： CloudSat Aqua 液态云 最优估计理论     

Dynamical Measurement's Uncertainty in the Curved Space‐Time

The dynamical characteristics of measurement's uncertainty are investigated under two modes of Dirac field in the Garfinkle–Horowitz–Strominger dilation space‐time. It shows that the Hawking effect induced by the thermal field would result in an expansion of the entropic uncertainty with increasing dilation‐parameter value, as the systemic quantum coherence reduces, reflecting that the Hawking effect could undermine the systemic coherence. Meanwhile, the intrinsic relationship between the uncertainty and quantum coherence is obtained, and it is revealed that the uncertainty's bound is anti‐correlated with the system's quantum coherence. Furthermore, it is illustrated that the systemic mixedness is correlated with the uncertainty to a large extent. Via the information flow theory, various correlations including quantum and classical aspects, which can be used to form a physical explanation on the relationship between the uncertainty and quantum coherence, are also analyzed. Additionally, this investigation is extended to the case of multi‐component measurement, and the applications of the entropic uncertainty relation are illustrated on entanglement criterion and quantum channel capacity. Lastly, it is declared that the measurement uncertainty can be quantitatively suppressed through optimal quantum weak measurement. These investigations might pave an avenue to understand the measurement's uncertainty in the curved space‐time.     

Controlling of Entropic Uncertainty in Qubits System Under the Generalized Amplitude Damping Channel via Weak Measurements

We study the effect of weak measurements on the entropic uncertainty in two-qubit system under the generalized amplitude damping channel. Our results show that, the entropic uncertainty in qubits system can be reduced under weak measurements by choosing appropriate measuring strength, which provides a new method to break through the restriction of uncertainty relation in quantum mechanics.     

光源功率谱对白光干涉测量的影响

本文从理论上分析了白光干涉测量中光源功率谱宽、包络函数、纵模形状和间隔等与干涉峰宽度、周期间的关系，从而讨论了空间干涉法在保偏光纤参数测量和传感应用中光源功率谱参数对测量分辨率、动态范围等的影响。     

量子真空计量标准中的非极性稀薄气体折射率测量研究

为进一步提高真空量值的复现性和准确性,最新研究采用量子技术实现对真空量值的测量与表征.该方法利用Fabry-Perot谐振腔实现腔内气体折射率的精密测量,并反演出气体密度,进而获得对应的真空量值,其中气体折射率的测量是影响真空量值准确性的关键.本文基于第一性原理,利用从头计算理论计算了在已知压力和温度条件下的氦气折射率,给出腔内气体压力与折射率关系的表达式,并利用基于Fabry-Perot激光谐振腔的真空测量装置,通过双腔谐振激光拍频精确测量了充气前后谐振激光频率的变化,测出了氦气折射率,并分析了测量不确定度.将理论计算值与实验测量值进行了对比分析,得出了制约准确度提高的主要因素,并提出了修正方法.     

广义测不准关系与三维BTZ黑洞熵

通过应用在量子引力中,由广义测不准关系得出的新的态密度方程,研究三维BTZ背景下黑洞的熵.当取广义测不准关系中引入的,具有Planck量级与空间维数有关的常数λ为特定值时,得到BTZ黑洞Bekenstein-Hawking 熵和修正项.由于利用新的态密度方程,在计算中不存在用brick-wall模型计算黑洞熵时出现的发散项和小质量近似.所得结论,从量子统计力学角度给出了黑洞Bekenstein-Hawking 熵的修正值,使人们对黑洞熵的修正值有更深入的认识. 关键词： 广义测不准关系 量子统计 BTZ黑洞熵     

Quantum Reality and Measurement: A?Quantum?Logical Approach

The recently established universal uncertainty principle revealed that two nowhere commuting observables can be measured simultaneously in some state, whereas they have no joint probability distribution in any state. Thus, one measuring apparatus can simultaneously measure two observables that have no simultaneous reality. In order to reconcile this discrepancy, an approach based on quantum logic is proposed to establish the relation between quantum reality and measurement. We provide a language speaking of values of observables independent of measurement based on quantum logic and we construct in this language the state-dependent notions of joint determinateness, value identity, and simultaneous measurability. This naturally provides a contextual interpretation, in which we can safely claim such a statement that one measuring apparatus measures one observable in one context and simultaneously it measures another nowhere commuting observable in another incompatible context.     

Generalized information theoretic measure to discern the quantumness of correlations

A novel measure, quantumness of correlations Q_AB is introduced here for bipartite states, by incorporating the required measurement scheme crucial in defining any such quantity. Quantumness coincides with the previously proposed measures in special cases and it vanishes for separable states--a feature not captured by the measures proposed earlier. It is found that an optimal generalized measurement on one of the parts leaves the overall state in its closest separable form, which shares the same marginal for the other part, implying that Q_AB is nonzero for all entangled bipartite states and it serves as an upper bound to the relative entropy of entanglement.     

Application for optical thermometers calibration based on virtual instruments

In this paper we present a new developed application for calibration of optical thermometers which is implemented in the Serbian Metrology Institute. The method for calibration of optical thermometer–pyrometer is based on measuring blackbody temperature via thermocouple standards and measuring voltage on pyrometer in temperature range from 550 to 1650 °C. The objective is to precisely determinate calibration curve of pyrometer—transfer function. The metrology traceability was realized through thermocouples standard which has traceability to the international standard. A developed application has a role to control and supervise calibration process. Based on virtual instruments (VI), application offers monitoring measurement parameters in real time on three charts. The main advantage of the developed VI application is reduction of measurement uncertainty of type A by increased accuracy with multi—temperature measurement up to 3 thermocouples on temperature equilibrium in the measurement system and automatic data processing by converting voltage to temperature, calculating the mean value and standard deviation of the mean value. Advantage is also reflected in permanent data logging while application is running and low cost and user friendly interface One of the goals is to improve quality of metrological services through this application and support the establishment of a traceability chain to SI.     

Nonperturbative theory of weak pre- and post-selected measurements

This paper starts with a brief review of the topic of strong and weak pre- and post-selected (PPS) quantum measurements, as well as weak values, and afterwards presents original work. In particular, we develop a nonperturbative theory of weak PPS measurements of an arbitrary system with an arbitrary meter, for arbitrary initial states of the system and the meter. New and simple analytical formulas are obtained for the average and the distribution of the meter pointer variable. These formulas hold to all orders in the weak value. In the case of a mixed preselected state, in addition to the standard weak value, an associated weak value is required to describe weak PPS measurements. In the linear regime, the theory provides the generalized Aharonov–Albert–Vaidman formula. Moreover, we reveal two new regimes of weak PPS measurements: the strongly-nonlinear regime and the inverted region (the regime with a very large weak value), where the system-dependent contribution to the pointer deflection decreases with increasing the measurement strength. The optimal conditions for weak PPS measurements are obtained in the strongly-nonlinear regime, where the magnitude of the average pointer deflection is equal or close to the maximum. This maximum is independent of the measurement strength, being typically of the order of the pointer uncertainty. In the optimal regime, the small parameter of the theory is comparable to the overlap of the pre- and post-selected states. We show that the amplification coefficient in the weak PPS measurements is generally a product of two qualitatively different factors. The effects of the free system and meter Hamiltonians are discussed. We also estimate the size of the ensemble required for a measurement and identify optimal and efficient meters for weak measurements. Exact solutions are obtained for a certain class of the measured observables. These solutions are used for numerical calculations, the results of which agree with the theory. Moreover, the theory is extended to allow for a completely general post-selection measurement. We also discuss time-symmetry properties of PPS measurements of any strength and the relation between PPS and standard (not post-selected) measurements.     

双线阵CCD交汇测量系统结构优化与精度分析

双线阵CCD交汇测量系统在检测目标着靶点坐标方面具有十分广泛的应用。在介绍双线阵CCD交汇测量原理的基础上,综合分析了交汇测量精度与系统结构参数之间的关系,建立了相应的数学模型,给出了最优结构参数设计的方法。利用计算机仿真技术对其进行了分析,得出在相应技术指标要求情况下的最优化系统结构,并给出了靶面坐标测量误差的三维分布图。     

一种太赫兹脉冲探测芯片性能分析

针对一种已经完成模拟设计、工艺研究及成品开发,且线度仅为百μm量级的太赫兹脉冲热载流子探测芯片展开了几何参数及电参数测试,并对其性能进行了分析探讨。结果表明:探测芯片具有较小的几何加工偏差和良好的欧姆接触效果;模拟计算的结果表明这种量级几何加工偏差对相对灵敏度影响可以忽略;综合分析各种测试测量结果,进一步验证了芯片开发工艺和测试结果的有效性。     

噪声对等光频采样调频连续波激光雷达测距精度的影响分析及实验验证

调频连续波激光雷达具有测量范围大,精度高,无需合作目标等优点,在计量学和工业现场测量中具有重要作用。简单介绍了等光频重采样调频连续波激光雷达的基本结构和测距原理,分析了系统辅助干涉信号和测量干涉信号中存在的主要噪声及其特点。当系统辅助干涉信号中存在噪声时,会造成极值点不准确并且引入测量误差。随后,使用Cramér-Rao下界定理评估测量干涉信号的噪声对测量结果的影响。为了提高测量的准确性和稳定性,基于经验模态分解的小波阈值滤波和汉宁窗带通滤波结合小波滤波的自适应滤波方法分别用来去除了辅助干涉信号和测量干涉信号中的噪声。实验中多次测量了平面镜和多种粗糙度样块,并使用精密导轨验证测量结果的准确性。实验结果表明,当被测物位于3.9 m左右时,使用自适应滤波方法去除噪声后,系统对反射镜和其他粗糙度样块的测量不确定度为20 μm和几十微米(K取值2),远小于使用小波阈值滤波的方法(120 μm和几百微米)。同时,通过对比精密导轨位移数值和系统的测量结果,证明了所提出的方法能够有效提高系统的测量准确性。     

Measurement of thermal rise-time of a laser diode based on spectrally resolved waveforms

Thermal resistance and thermal rise-time are two basic parameters that affect most of the performances of a laser diode greatly. By measuring waveforms received after a spectroscope at wavelengths varied step-by-step, the spectrally resolved waveforms can be converted to calculate the thermal rise-time. Basic formulas for the spectrum variation of a laser diode and the measurement set-up by using a Boxcar are described in the paper. As an example, the thermal rise-time of a p-side up packaged short-pulse laser diode was measured by the method to be 390 μs. The method will be useful in characterizing diode lasers and LD modules in high-power applications.     

Can Sobolev Inequality Be Written for Sharma-Mittal Entropy?

In this paper, we focus on Sobolev inequality in the context of Sharma-Mittal entropy. Using this new inequality, generalized entropic uncertainty relation in accordance with Sharma-Mittal entropy is derived and the pseudoadditivity relation has been obtained. This new entropic uncertainty relation has then been applied to physical examples such as one dimensional harmonic oscillator and Pösch-Teller potential. Finally, it has been shown that for certain values of the parameters of Sharma-Mittal measure, the present results reduce to the corresponding results of Shannon, Renyi and Tsallis measures.     

基于广义动态约束的红外目标跟踪

采用广义方法研究红外目标跟踪中动态约束低效的问题,通过把测量点映射到值域的函数集,建立约束关系,接着对跟踪模型中的变换参量通过匹配点解出,最后对广义动态约束决策函数条件排序,同时修正约束条件,使整个系统在预定的时刻达到最佳跟踪效果。仿真实验表明该方法与动态约束算法相比能有效辨识动态目标,跟踪效果没有丢失现象。