Heisenberg's uncertainty principle

Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can be reconciled if an appropriate trade-off is accepted. The uncertainty principle is shown to appear in three manifestations, in the form of uncertainty relations: for the widths of the position and momentum distributions in any quantum state; for the inaccuracies of any joint measurement of these quantities; and for the inaccuracy of a measurement of one of the quantities and the ensuing disturbance in the distribution of the other quantity. Whilst conceptually distinct, these three kinds of uncertainty relations are shown to be closely related formally. Finally, we survey models and experimental implementations of joint measurements of position and momentum and comment briefly on the status of experimental tests of the uncertainty principle.     

Teleportation of n-Particle State via n Pairs of EPR Channels

The teleportation of an arbitrary n-particle state (n ≥ 1) is proposed if n pairs of identical EPR states are utilized as quantum channels. Independent Bell state measurements are performed for joint measurement. By using a special Latin square of order 2n(n ≥ 1), explicit expressions of outcomes after the Bell state measurements by Alice (sender) and the corresponding unitary transformations by Bob (receiver) can be derived. It is shown that the teleportation of n-particle state can be implemented by a series of single-qubit teleportation.     

Multiparty-controlled Joint Remote Preparation of an Arbitrary m-qudit State with d-dimensional Greenberger-Horne-Zeilinger States

We present a scheme for multiparty-controlled joint remote preparation of an arbitrary m-qudit state by using d-dimensional Greenberger-Horne-Zeilinger (GHZ) states as the quantum channel. An arbitrary m-qudit state can be transmitted from two senders to a remote receiver in a quantum communication network under the controller’s control. The senders perform m-qudit measurements according to their information of prepared state, the controllers only need perform single-particle projective measurements. The receiver can prepare the original state on his quantum system by performing corresponding unitary operation according the measurement results of the senders and controllers. It is shown that an arbitrary m-qudit state in general form can be controlled joint remote prepared if and only if the receiver cooperates with all the senders and controllers.     

Reducing backaction when measuring temporal correlations in quantum systems

Dynamic correlations of quantum observables are challenging to measure due to measurement backaction incurred at early times. Recent work [P. Uhrich et al., Phys. Rev. A 96, 022127 (2017)] has shown that ancilla-based noninvasive measurements are able to reduce this backaction, allowing for dynamic correlations of single-site spin observables to be measured. We generalise this result to correlations of arbitrary spin observables and extend the measurement protocol to simultaneous noninvasive measurements which allow for real and imaginary parts of correlations to be extracted from a single set of measurements. We use positive operator-valued measures to analyse the dynamics generated by the ancilla-based measurements. Using this framework we prove that special observables exist for which measurement backaction is of no concern, so that dynamic correlations of these can be obtained without making use of ancillas.     

Sensitivity and optimization in the determination of deformations by holographic interferometry

The use of a fringe-counting holographic interferometric technique for measuring small superficial displacements can present difficulties in determining the measurement inaccuracy. A useful general method is given here for the analysis of errors in displacement measurements. The optimum number and type of observation directions are determined and correspond to counting in the four semi-diagonals of the holographic plate. The technique, as applied to skull experiments, makes it possible to measure directly displacements of up to 20 μm, in the object plane parallel to the holographic plate. The associated errors range from 0.1–0.3 μm, for a counting inaccuracy of of a fringe and increments of traction of 100 g to 1 kg of force.     

Extracting Work Optimally with Imprecise Measurements

Measurement and feedback allows for an external agent to extract work from a system in contact with a single thermal bath. The maximum amount of work that can be extracted in a single measurement and the corresponding feedback loop is given by the information that is acquired via the measurement, a result that manifests the close relation between information theory and stochastic thermodynamics. In this paper, we show how to reversibly confine a Brownian particle in an optical tweezer potential and then extract the corresponding increase of the free energy as work. By repeatedly tracking the position of the particle and modifying the potential accordingly, we can extract work optimally, even with a high degree of inaccuracy in the measurements.     

Some problems on the measurement of quantum observables and determination of joint entropy in quantum statistics

In the paper the equivalency of a successive measurement of observablesa andb on the Hilbert spaceH and a specially organized measurement of the observablea⊗b on the Hilbert space ℋ=H⊗H is determined. The state, wherein the measurement on ℋ is performed, is shown to be an operator analog of classical joint density of probability distribution. The functionals such as joint and conventional entropy are constructed; the entropy defect of a quantum ensemble and the information quantity contained in quantum measurement are determined.     

Quantum information and microscopic measuring instruments

The consideration of measuring instruments as macroscopic bodies leads to neglect of the microscopic processes that occur during measurements. This disregard is not justified in general cases. As an example of measurements using microscopic instruments, the scattering of a photon by an electron with electron interference at two slits(Compton effect) was used. The amount of information that can be obtained in such a process is inversely proportional to the wavelength of the incident photon. At large photon wavelengths(soft measurements), the pure state of the electron can be disrupted by an arbitrarily small extent; accordingly, the amount of information extracted in such an experiment is also arbitrarily small. It is shown that the energy price for a bit obtained in such a measurement tends toward a constant value for increasing the photon wavelength. Microscopic instruments can be used in situations where energy costs for measurements are important.     

无光栅频率分辨光学开关行迹分析

从无光栅频率分辨光学开关(GRENOUILLE)的测量原理出发,分析了不均匀的光束空间轮廓导致行迹畸变的原因,并通过数值方法模拟了GRENOUILLE内部存在的数据一致性校验机制对这种影响的抑制作用。结果表明:不均匀光束空间轮廓对GRENOUILLE测量结果的影响并不显著;实际测量中更应避免的是使用过小的光束口径,它将导致行迹不完整,从而显著影响时间波形的测量结果。     

电磁发射中固体电枢的磁探针测速误差

对磁探针感应电压的原理进行分析,得出电枢电流变化率是磁探针测量电枢膛内运动位置误差的原因。通过简化,采用理想化的电枢电流波形和电枢位移曲线,不同电枢电流变化率条件下,在Matlab软件中对磁探针测量电枢位置进行仿真分析。结果表明:测量电枢位置误差与电枢电流变化率绝对值正相关,电枢电流变化率相同时,误差与电枢电流和电枢速度的乘积负相关。进一步对磁探针测量电枢膛内速度的误差进行仿真分析,理想电流曲线仿真结果表明:测速误差情况可分为三种,电枢电流变化率相近,则测速误差小,反之则测速误差大。     

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.     

Influence of experimental resolution on the quantum-to-classical transition in the quartic oscillator

The quantum-classical transition problem is investigated for the quartic oscillator coupled to a thermal reservoir. We show for this model that the combination of relevant diffusion, classical action (represented by the amplitude of an initial coherent state) and the experimental uncertainties is necessary to achieve the classical regime. In order to study the role of limited resolutions of measurement apparatuses on the correspondence between the quantum and classical dynamics, we consider experimental errors due the preparation of the initial state of the quartic oscillator and the inaccuracies in the time measurements. A quantum break time depending on the diffusion constant, the amplitude of the initial coherent state and the inaccuracy of measurements is defined. We found, for this model, a regime where the increasing of diffusion does not anticipate classicality. In such regime, there is a minimum value for the classical action associated to classical behavior of the system.     

Error Principle

The problem of characterizing the accuracy ofand disturbance caused by a joint measurement ofposition and momentum is investigated. In a previouspaper the problem was discussed in the context of the unbiased measurements considered by Arthurs andKelly. It is now shown that suitably modified versionsof these results hold for a much larger class ofsimultaneous measurements. The approach is a development of that adopted by Braginsky and Khalili in thecase of a single measurement of position only. Adistinction is made between the errors of retrodictionand the errors of prediction. Two error-errorrelationships and four error-disturbance relationships arederived, supplementing the uncertainty principle usuallyso-called. In the general case it is necessary to takeinto account the range of the measuring apparatus. Both the ideal case of an instrument havinginfinite range and the case of a real instrument forwhich the range is finite are discussed.     

Inaccurate experiments and environment-induced superselection rules

It is argued that approximate superselection rules induced by the environment cannot account for the emergence of definite measurement results in single experiments. The reason for this is that the inaccuracy necessary for an experiment failing to distinguish between exact and approximate mixtures requires the pointer observable to be strictly classical. This is shown in the case that the observables of physical systems generateW ^*-algebras.     

Heisenberg-limited Measurements and Sub-Planck Structures in Phase Space

It is shown how sub-Planck phase-space structures can be used to achieve Heisenberg-limited sensitivity in weak force measurements. Nonclassical states of harmonic oscillators, such as superpositions of coherent states, are shown to be useful for the measurement of weak forces that cause translations or rotations in phase space, which is done by entangling the quantum oscillator with a two-level system. This method is closely related to the Loschmidt echo techniques employed in nuclear magnetic resonance experiments. Implementations of this strategy in cavity QED and ion traps are described.     

Perceptual assimilation of Dutch vowels by Peruvian Spanish listeners

This work investigated the measurement of vibrato and tremor extent values. Related works have not explored the possibility of measuring extent in the spectra of fundamental frequency (f(0)) low-frequency undulations. It is shown here that by canceling average (DC) values and baseline drifts of f(0) contours, as well as weighting the respective spectra by the time window DC value, extent measures can be promptly obtained in the frequency domain. The method is illustrated with measurements from synthetic and human data.     

机械臂D-H参数和减速比几何标定及误差补偿

针对机械臂D-H参数和关节电机减速比不精确导致机械臂绝对定位精度降低的问题,提出了在利用几何分析标定机械臂D-H参数的基础上,通过分析关节实际旋转角度和相应电机编码器码值的线性关系,标定关节电机减速比的方法。针对关节角误差微分补偿法计算量大的缺点,通过推导机械臂末端位姿矩阵误差和关节角误差之间的微分关系建立误差模型,求解关节补偿角,避免了雅各比矩阵的求取,提高了计算效率。最后采用三维激光跟踪仪搭建测量系统,完成了一种6自由度机械臂的标定及补偿实验。实验结果表明,通过参数标定及误差补偿,机械臂的绝对定位误差均值从标定前的2.83 mm和1.14°降低到0.54 mm和0.24°,验证了方法的有效性。