Entropic uncertainty relations for angular distributions

A new entropic uncertainty relation for simultaneous measurements of two angles ? and θ and two corresponding angular momentum operators L_z and L² is derived. Step function techniques are introduced to complete the proof.     

Generalized quantum measurements and approximate simultaneous measurements of noncommuting observables

The importance of generalized quantum measurements in quantum optics and precision measurements is indicated. These measurements are formally realizable within conventional quantum mechanics and can often be interpreted as approximate simultaneous measurements of noncommuting observables. An uncertainty relation more stringent than the usual one is derived for these measurements.     

An Informational Characterization of Schrödinger's Uncertainty Relations

Heisenberg's uncertainty relations employ commutators of observables to set fundamental limits on quantum measurement. The information concerning incompatibility (non-commutativity) of observables is well included but that concerning correlation is missing. Schrödinger's uncertainty relations remedy this defect by supplementing the correlation in terms of anti-commutators. However, both Heisenberg's uncertainty relations and Schrödinger's uncertainty relations are expressed in terms of variances, which are not good measures of uncertainty in general situations (e.g., when mixed states are involved). By virtue of the Wigner–Yanase skew information, we will establish an uncertainty relation along the spirit of Schrödinger from a statistical inference perspective and propose a conjecture. The result may be interpreted as a quantification of certain aspect of the celebrated Wigner–Araki–Yanase theorem for quantum measurement, which states that observables not commuting with a conserved quantity cannot be measured exactly.     

Unification theory of classical statistical uncertainty relation and quantum uncertainty relation and its applications

General classical statistical uncertainty relation is deduced and generalized to quantum uncertainty relation. We give a general unification theory of the classical statistical and quantum uncertainty relations, and prove that the classical limit of quantum mechanics is just classical statistical mechanics. It is shown that the classical limit of the general quantum uncertainty relation is the general classical uncertainty relation. Also, some specific applications show that the obtained theory is self-consistent and coincides with those from physical experiments.     

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.     

Conditional expectations,conditional distributions,anda posteriori ensembles in generalized probability theory

A general probabilistic framework containing the essential mathematical structure of any statistical physical theory is reviewed and enlarged to enable the generalization of some concepts of classical probability theory. In particular, generalized conditional probabilities of effects and conditional distributions of observables are introduced and their interpretation is discussed in terms of successive measurements. The existence of generalized conditional distributions is proved, and the relation to M. Ozawa'sa posteriori states is investigated. Examples concerning classical as well as quantum probability are discussed.     

Quantum-Memory-Assisted Entropic Uncertainty Relation and Quantum Coherence in Structured Reservoir

The uncertainty principle is regarded as one of basics in quantum mechanics, which sets up a strict lower bound to quantify the prediction on the outcome concerning a set of incompatible measurements. In this paper, we investigate the dynamic behaviors of quantum-memory-assisted entropic uncertainty relation (EUR), and quantum coherence in structured reservoir. The results shown that the EUR is smallest in the vanishing limit of noise regardless of the forms of the initial sate we considered, while the coherence keeps the maximal value. During the time-evolution process, the uncertainty bound is lifted and the coherence damps monotonously. Subsequently, the EUR converges to an asymptotic nonzero constant in the long-time limit, yet the coherence asymptotically decays to zero. Moreover, the initial state purity plays a deterministic role in the initial amounts of EUR and coherence, i.e. the larger purity the less EUR and larger coherence. As an application, we employ the EUR to witness the coherence, and prove that the corresponding witnessing efficiencies are only depended on the version of coherence, while are insensitive to the reservoir.

     

Autocorrelation function formulations and the turbulence dissipation rate: Application to dispersion models

The classical statistical diffusion theory and the binomial autocorrelation function are used to obtain a new formulation for the turbulence dissipation rate ε. The approach employs the Maclaurin series expansion of a logarithm function contained in the dispersion parameter formulation. The numerical coefficient of this new relation for ε is 100% larger than the numerical coefficient of the classical relation derived from the exponential autocorrelation function. A similar approach shows that the dispersion parameter obtained from the even exponential autocorrelation function does not result in a relation for ε and, therefore, is not suitable for application in dispersion models. In addition, a statistical comparison to experimental ground-level concentration data demonstrates that this newly derived relation for ε as well as other formulations for the turbulence dissipation rate are suitable for application in Lagrangian stochastic dispersion models. Therefore, the analysis shows that there is an uncertainty regarding the turbulence dissipation rate function form and the autocorrelation function form.     

Ni I oscillator strengths

Oscillator strengths of 150 Ni I lines in the spectral range 2800–6200 Å have been obtained by emission and from hook measurements. Relative sets of ?-values were determined by combining emission measurements on a hollow cathode with hook measurements in a high-temperature furnace. No assumption concerning the plasma state is used, and no temperature determination is required. The relative measurements have been placed on an absolute scale by using lifetime data. The uncertainty of the ?-values is 13% on average. Comparisons are made with the results of other authors.     

Analyzing statistical errors for measurements of Brillouin scattering by the edge technique

The signal estimate and statistical uncertainty in the measurements of Brillouin shift by the edge technique are analyzed in detail. A signal to noise parameter factor is introduced and is used to discuss the statistical uncertainty in the measurements. The effect of signal averaging and the effect due to background noise are analyzed. Some helpful conclusions are predicted. PACS 42.68.Wt; 42.79.Qx; 78.35.+c     

The Measurement-Disturbance Relation and the Disturbance Trade-off Relation in Terms of Relative Entropy

We employ quantum relative entropy to establish the relation between the measurement uncertainty and its disturbance on a state in the presence (and absence) of quantum memory. For two incompatible observables, we present the measurement-disturbance relation and the disturbance trade-off relation. We find that without quantum memory the disturbance induced by the measurement is never less than the measurement uncertainty and with quantum memory they depend on the conditional entropy of the measured state. We also generalize these relations to the case with multiple measurements. These relations are demonstrated by two examples.     

Objective uncertainty relation with classical background in a statistical model

We show within a statistical model of quantization reported in the previous work based on Hamilton–Jacobi theory with a random constraint that the statistics of fluctuations of the actual trajectories around the classical trajectories in velocity and position spaces satisfy a reciprocal uncertainty relation. The relation is objective (observation independent) and implies the standard quantum mechanical uncertainty relation.     

An uncertainty relation for joint position-momentum measurements

It is shown that the lower bound in the uncertainty relation for joint position-momentum measurements is twice as large as that in the usual Heisenberg uncertainty principle for separate measurements.     

The remaining uncertainty in quantum measurement of noncommuting discrete observables

The quantum mechanical measuring process is analyzed from the standpoint of information theory. We determined the remaining uncertainty in the successive measurements of two discrete noncommuting observables and found its lower bound. Using this lower bound, a new simple form of uncertainty relation for two discrete noncommuting observables is proposed.     

Pressure,temperature and light influence on spin transition solids

Abstract

Present paper is an overview of our efforts during the past few years to understand complicated corelations of physical phenomena related to pressure in Fe(I1) solid state spin transition systems. Some principal results concerning p, T, λ-experiments are extracted. In the context of correlation of the crystallographic phase transition with simultaneous HS → LS relaxation and LS → HS photopopulation, we show the latest results: Brillouin and magnetic measurements on the crystal [Fe(pt₆](BF₆)₂.     

相干与信息守恒及其在Mach-Zehnder干涉中的应用

自量子力学诞生以来,相干性和互补性一直是被广泛而深入研究的两个重要课题.随着量子信息近年来的发展,人们引入了若干度量来定量地刻画相干性和互补性.本文建立两个信息守恒关系式,分别基于"Bures距离-保真度"和"对称-非对称",并且利用它们来刻画相干性和互补性.具体来说,首先从信息守恒的观点解释Bures距离和保真度的互补关系,并由此自然推导出Mach-Zehnder干涉仪中的Englert"干涉-路径"互补关系.其次在量子态和信道相互作用的一般框架中讨论"对称-非对称"信息守恒关系,并揭示其与Bohr互补性和量子相干性的内在联系.最后,在Mach-Zehnder干涉仪中探讨相干、退相干及互补性,刻画两个信息守恒关系之间的密切联系.     

Lidar calibration experiments

A series of atmospheric aerosol diffusion experiments combined with lidar detection was conducted to evaluate and calibrate an existing retrieval algorithm for aerosol backscatter lidar systems. The calibration experiments made use of two (almost) identical mini-lidar systems for aerosol cloud detection to test the reproducibility and uncertainty of lidars. Lidar data were obtained from both single-ended and double-ended lidar configurations. A backstop was introduced in one of the experiments and a new method was developed where information obtained from the backstop can be used in the inversion algorithm. Independent in-situ aerosol plume concentrations were obtained from a simultaneous tracer gas experiment with SF, and comparisons with the two lidars were made. The study shows that the reproducibility of the lidars is within 15%, including measurements from both sides of a plume. The correspondence with in-situ measurements is excellent. Finally, the new backstop method is able to reveal information which can close the lidar equation by obtaining the relation between backscatter and extinction in an aerosol cloud. Received: 21 December 1995 / Revised version: 25 July 1996     

Instantaneous in-flame measurement of soot volume fraction, primary particle diameter, and aggregate radius of gyration via auto-compensating laser-induced incandescence and two-angle elastic light scattering

A new combination of soot diagnostics employing two-angle elastic light scattering and laser-induced incandescence is described that is capable of producing non-intrusive, instantaneous, and simultaneous, in situ measurements of soot volume fraction, primary particle size, and aggregate radius of gyration within flames. Controlled tests of the new apparatus on a well-characterized laminar flame show good agreement with existing measurements in the literature. From a detailed and comprehensive Monte Carlo uncertainty analysis of the results, it was found that the uncertainty in all three measured parameters is dominated by knowledge of soot properties and aggregation behavior. The soot volume fraction uncertainty is dominated by uncertainty in the soot refractive index light absorption function; the primary particle diameter uncertainty is dominated by uncertainty in the fractal prefactor; while the uncertainty in the aggregate radius of gyration is dominated by the uncertainty in the width of the distribution of aggregate sizes.     

Uncertainty relation of successive measurements based on Wigner–Yanase skew information

Wigner-Yanase skew information could quantify the quantum uncertainty of the observables that are not commuting with a conserved quantity.We present the uncertainty principle for two successive projective measurements in terms of Wigner-Yanase skew information based on a single quantum system.It could capture the incompatibility of the observables,i.e.the lower bound can be nontrivial for the observables that are incompatible with the state of the quanaim system.Furthermore,the lower bound is also constrained by the quantum Fisher information.In addition,we find the complementarity relation between the uncertainties of the observable which operated on the quantum state and the other observable that performed on the post-measured quantum state and the uncertainties formed by the non-degenerate quantum observables performed on the quantum state,respectively.