Wave-mechanical uncertainty and speed limitations

The results of a recent study on the limiting uncertainties in the measurement of photon radiation dose with MOSFET dosimeters are reported. The statistical uncertainty in dose measurement from a single device has been measured before and after irradiation. The resulting increase in 1/f noise with radiation dose has been investigated via various analytical models. The limit of uncertainty in the ubiquitous linear trend of threshold voltage with dose has been measured and compared to two nonlinear models. Inter-device uncertainty has been investigated in a group of 40 devices, and preliminary evidence for kurtosis and skewness in the distributions for devices without external bias has been observed.

As a very fundamental principle in quantum physics, uncertainty principle has been studied intensively via various uncertainty inequalities. A natural and fundamental question is whether an equality exists for the uncertainty principle. Here we derive an entropic uncertainty equality relation for a bipartite system consisting of a quantum system and a coupled quantum memory, based on the information measure introduced by Brukner and Zeilinger (Phys. Rev. Lett. 83:3354, 1999). The equality indicates that the sum of measurement uncertainties over a complete set of mutually unbiased bases on a subsystem is equal to a total, fixed uncertainty determined by the initial bipartite state. For the special case where the system and the memory are the maximally entangled, all of the uncertainties related to each mutually unbiased base measurement are zero, which is substantially different from the uncertainty inequality relation. The results are meaningful for fundamental reasons and give rise to operational applications such as in quantum random number generation and quantum guessing games. Moreover, we experimentally verify the measurement uncertainty relation in the presence of quantum memory on a five-qubit spin system by directly measuring the corresponding quantum mechanical observables, rather than quantum state tomography in all the previous experiments of testing entropic uncertainty relations.

In the context of small molecule property prediction, experimental errors are usually a neglected aspect during model generation. The main caveat to binary classification approaches is that they weight minority cases close to the threshold boundary equivalently in distinguishing between activity classes. For example, a pXC50 activity value of 5.1 or 4.9 are treated equally important in contributing to the opposing activity (e.g., classification threshold of 5), even though experimental error may not afford such discriminatory accuracy. This is detrimental in practice and therefore it is equally important to evaluate the presence of experimental error in databases and apply methodologies to account for variability in experiments and uncertainty near the decision boundary. In order to improve upon this, we herein present a novel approach toward predicting protein-ligand interactions using a Probabilistic Random Forest (PRF) classifier. The PRF comprises a modification to the long-established Random Forest (RF), to take into account uncertainties in the assigned classes (i.e., activity labels). This enables representing the activity in a framework in-between the classification and regression architecture, with philosophical differences from either approach. Compared to classification, this approach enables better representation of factors increasing/decreasing inactivity. Conversely, one can utilize all data (even delimited/operand/censored data far from a cut-off) at the same time as taking into account the granularity around the cut-off, compared to a classical regression framework. The algorithm was applied toward ~550 target prediction tasks from ChEMBL and PubChem. The largest benefit in incorporating the experimental deviation in PRF was observed for data points close to the binary threshold boundary, when such information is not considered in any way in the original RF algorithm. In comparison, the baseline RF outperformed PRF for cases with high confidence to belong to the active class (far from the binary decision threshold). The RF models gave errors smaller than the experimental uncertainty, which could indicate that they are overtrained and/or over-confident. Overall, we show that PRF can be useful for target prediction models in particular for data where class boundaries overlap with the measurement uncertainty, and where a substantial part of the training data is located close to the classification threshold. With this approach, we present, to our knowledge, for the first time an application of probabilistic modelling of activity data for target prediction using the PRF algorithm.

The uncertainty principle states that the amount of uncertainty of a particle’s velocity multiplied by the amount of uncertainty of a particle’s position is a constant. In other words, the more certain about particle’s velocity, the less certain about particle’s position and vice versa. This paper will focus on the uncertainty measure is not a constant but a variable quantity. The uncertainty principle is situation based realism. In certain situations, it is more and in certain situations, it is less. The variable uncertainty principle is the total amount of uncertainty of position and velocity multiplied by the total amount of certainty of position and velocity is a constant. I will also discuss that the physical time is a complex quantity and the variable uncertainty principle actually depends on the complex physical time. The complex physical time has two parts - the real physical time and the imaginary physical time.

Uncertainty measures must not depend on the choice of origin of the measurement scale; it is therefore argued that quantum-mechanical uncertainty relations, too, should remain invariant under changes of origin. These points have often been neglected in dealing with angle observables. Known measures of location and uncertainty for angles are surveyed. The angle variance angv {o} is defined and discussed. It is particularly suited to the needs of quantum theory, because of its affinity to the Hilbert space metric, and its use of the basic sine and cosine operators. Corresponding uncertainty relations involving azimuthal or phase angles are indicated, and their relevance to study and definition of coherent states is briefly reviewed.

Evaluation of uncertainty and detection limits in 210Pb and 210Po measurement in water by alpha spectrometry using 210Po spontaneous deposition onto a silver disk

One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty principle from two comprehensible assumptions: impossibility of instantaneous messaging at a distance (no-signaling), and violation of Bell inequalities (nonlocality). The uncertainty is established for a pair of observables of one of two spatially separated systems that exhibit nonlocal correlations. To this end, we introduce a gentle form of measurement which acquires partial information about one of the observables. We then bound disturbance of the remaining observables by the amount of information gained from the gentle measurement, minus a correction depending on the degree of nonlocality. The obtained quantitative expression resembles the quantum mechanical formulations, yet it is derived without the quantum formalism and complements the known qualitative effect of disturbance implied by nonlocality and no-signaling.

We use a spectrum interpolation technique to improve the distributed strain measurement accuracy in a Rayleigh-scatter-based optical frequency domain reflectometry sensing system. We demonstrate that strain accuracy is not limited by the "uncertainty principle" that exists in the time-frequency analysis. Different interpolation methods are investigated and used to improve the accuracy of peak position of the cross-correlation and, therefore, improve the accuracy of the strain. Interpolation implemented by padding zeros on one side of the windowed data in the spatial domain, before the inverse fast Fourier transform, is found to have the best accuracy. Using this method, the strain accuracy and resolution are both improved without decreasing the spatial resolution. The strain of 3μϵ within the spatial resolution of 1cm at the position of 21.4m is distinguished, and the measurement uncertainty is 3.3μϵ.

The orthogonal superposition (OSP) technique is advantageous for measuring structural dynamics in complex fluids subjected to a primary shear flow. This technique superimposes a small-amplitude oscillation orthogonal to a primary shear flow to measure the real and imaginary components of the complex shear modulus. The commercial availability of OSP geometries and bi-axial transducers is expected to increase its adoption as a more routine rheological technique. It is important to understand calibration procedures and the influence of intrinsic inhomogeneous flow fields, residual pumping flow effects, and boundary forces at the leading edges of the geometry components on experimental error and measurement uncertainty. In this work, we perform calibration measurements of viscosity standards on a commercial shear rheometer using a double-wall concentric cylinder geometry. Newtonian calibration fluids with viscosities that range from 0.01 to 331 Pa s are used to obtain the end-effect factors in primary steady shear and orthogonal oscillatory shear directions. The corrections needed for the viscosity measured in steady shear range from 16 to 21%; whereas for the orthogonal complex viscosity, the errors range from 19 to 25%. Computational fluid dynamics simulations are used to understand the relationship between the end-effect corrections, OSP flow cell, and the imposed shear flow fields. We show that approximate linear shear deformation profiles are attained, in the double gap, for both primary rotational shear and orthogonal oscillatory shear deformation, with only a slight deviation for the fluid in the vicinity of the bob ends. We also present information on the velocity, pressure, and shear rate distributions for fluid within the entire flow cell. The overestimation of the orthogonal viscosity is attributed to the pressure forces exerted on the bob end surfaces (9%) and a higher shear rate in the double gap that leads to higher viscous stresses on the bob cylindrical surfaces (8%). The Newtonian fluid field information provides a benchmark for future simulations involving non-Newtonian fluids. Additionally, the operational knowledge (i.e., consistent sample filling) and measurement window (i.e., viscosity and frequency) described within are critical for proper use of the instrument and measurement accuracy.

Bipartite entanglement is one of the fundamental quantifiable resources of quantum information theory. We propose a new application of this resource to the theory of quantum measurements. According...

While some of the deepest results in nature are those that give explicit bounds between important physical quantities, some of the most intriguing and celebrated of such bounds come from fields where there is still a great deal of disagreement and confusion regarding even the most fundamental aspects of the theories. For example, in quantum mechanics, there is still no complete consensus as to whether the limitations associated with Heisenberg's Uncertainty Principle derive from an inherent randomness in physics, or rather from limitations in the measurement process itself, resulting from phenomena like back action. Likewise, the second law of thermodynamics makes a statement regarding the increase in entropy of closed systems, yet the theory itself has neither a universally-accepted definition of equilibrium, nor an adequate explanation of how a system with underlying microscopically Hamiltonian dynamics (reversible) settles into a fixed distribution. Motivated by these physical theories, and perhaps their inconsistencies, in this thesis we use dynamical systems theory to investigate how the very simplest of systems, even with no physical constraints, are characterized by bounds that give limits to the ability to make measurements on them. Using an existing interpretation, we start by examining how dissipative systems can be viewed as high-dimensional lossless systems, and how taking this view necessarily implies the existence of a noise process that results from the uncertainty in the initial system state. This fluctuation-dissipation result plays a central role in a measurement model that we examine, in particular describing how noise is inevitably injected into a system during a measurement, noise that can be viewed as originating either from the randomness of the many degrees of freedom of the measurement device, or of the environment. This noise constitutes one component of measurement back action, and ultimately imposes limits on measurement uncertainty. Depending on the assumptions we make about active devices, and their limitations, this back action can be offset to varying degrees via control. It turns out that using active devices to reduce measurement back action leads to estimation problems that have non-zero uncertainty lower bounds, the most interesting of which arise when the observed system is lossless. One such lower bound, a main contribution of this work, can be viewed as a classical version of a Heisenberg uncertainty relation between the system's position and momentum. We finally also revisit the murky question of how macroscopic dissipation appears from lossless dynamics, and propose alternative approaches for framing the question using existing systematic methods of model reduction.

Traditional computer experiments using emulators have treat the emulator output as containing no error; however, this is not always feasible, as there exist computational codes which produce stochastic output, and future computations may require a balance between the time or resources to run the code and the accuracy of the output. This paper proposes a framework for incorporating both computational uncertainty and observational uncertainty into an analysis using a Gaussian process regression and calibration, and provides an example using simulated output from the one-dimensional diffusion equation. The particular values of observational and computation uncertainty which minimize a cost function are obtained.

Uncertainty principle is at the heart of quantum physics, taking a fundamental and crucial role in the area of quantum information science, and it provides a remarkable lower bound to quantify our prediction for the measured outcome of two incompatible observables. Herein, the relationship between the lower bound of the measured uncertainty and quantum coherence is investigated under a one-dimensional Heisenberg XXZ spin model with Dzyaloshinskii–Moriya (DM) interactions, and the effect of DM interaction on the entropic uncertainty is also examined in details. We reveal the systematic temperature can give rise to the increase in the measurement uncertainty of interest at thermal equilibrium. By contrast, the stronger coupling strength $$ \left| J \right| $$ or the stronger DM interaction would induce the decrease in the amount with respect to the uncertainty. Moreover, we analyze the dynamical behaviors of quantum coherence and find that the bound of the uncertainty is oppositely correlated with the quantum coherence dramatically. Further, the effects of DM interaction along x-direction (characterized by the parameter Dx) and z-direction (characterized by Dz) on the uncertainty of interest are discussed, respectively. For the antiferromagnetic frame J > 0, it is interesting to obtain that x-direction DM interaction Dx exhibits a more powerful influence on reducing the uncertainty and enhancing the systematic coherence, when comparing with that of Dz. With these in mind, we wish our investigations would better understand the dynamical features of the measured uncertainty in the spin-based solid systems.

The well-known Robertson-Schr\"odinger uncertainty relations miss an irreducible lower bound. This is widely attributed to the lower bound's state dependence. Therefore, Abbott et al. introduced a general approach to derive tight state-independent uncertainty relations for qubit measurements [Mathematics 4, 8 (2016)]. The relations are expressed in two measures of uncertainty, which are standard deviation and entropy, both functions of the expectation value. Here, we present a neutron polarimetric test of the tight state-independent preparation uncertainty relations for orthogonal, as well as nonorthogonal, Pauli spin observables. The final results, obtained with pure and mixed spin states, reproduce the theoretical predictions clearly for arbitrary initial states of variable degree of polarization.

This paper aims at investigating the influence of space-time curvature on the uncertainty relation. In particular, relying on previous findings, we assume the quantum wave function to be confined to a geodesic ball on a given space-like hypersurface whose radius is a measure of the position uncertainty. On the other hand, we concurrently work out a viable physical definition of the momentum operator and its standard deviation in the non-relativistic limit of the 3+1 formalism. Finally, we evaluate the uncertainty relation which to second order depends on the Ricci scalar of the effective 3-metric and the corresponding covariant derivative of the shift vector. For the sake of illustration, we apply our general result to a number of examples arising in the context of both general relativity and extended theories of gravity.