Understanding linear measure

This article provides strategies for enhancing tasks to offer students better opportunities to develop conceptual understanding of length measurement. Teachers are offered strategies that help move instruction beyond procedures

Optimal measurement strategies for linear stochastic systems

Iterative digital computer algorithm for solving optimization problems for linear stochastic system

Uncollapsing the wavefunction by undoing quantum measurements

We review and expand on recent advances in theory and experiments concerning the problem of wavefunction uncollapse: Given an unknown state that has been disturbed by a generalized measurement, restore the state to its initial configuration. We describe how this is probabilistically possible with a subsequent measurement that involves erasing the information extracted about the state in the first measurement. The general theory of abstract measurements is discussed, focusing on quantum information aspects of the problem, in addition to investigating a variety of specific physical situations and explicit measurement strategies. Several systems are considered in detail: the quantum double dot charge qubit measured by a quantum point contact (with and without Hamiltonian dynamics), the superconducting phase qubit monitored by a SQUID detector, and an arbitrary number of entangled charge qubits. Furthermore, uncollapse strategies for the quantum dot electron spin qubit, and the optical polarization qubit are also reviewed. For each of these systems the physics of the continuous measurement process, the strategy required to ideally uncollapse the wavefunction, as well as the statistical features associated with the measurement is discussed. We also summarize the recent experimental realization of two of these systems, the phase qubit and the polarization qubit.Comment: 19 pages, 4 figure

Ordered Measurements of Permutationally-Symmetric Qubit Strings

We show that any sequence of measurements on a permutationally-symmetric (pure or mixed) multi-qubit string leaves the unmeasured qubit substring also permutationally-symmetric. In addition, we show that the measurement probabilities for an arbitrary sequence of single-qubit measurements are independent of how many unmeasured qubits have been lost prior to the measurement. Our results are valuable for quantum information processing of indistinguishable particles by post-selection, e.g. in cases where the results of an experiment are discarded conditioned upon the occurrence of a given event such as particle loss. Furthermore, our results are important for the design of adaptive-measurement strategies, e.g. a series of measurements where for each measurement instance, the measurement basis is chosen depending on prior measurement results.Comment: 13 page

Design of general-purpose sampling strategies for geometric shape measurement

Quality inspection is a preliminary step for different further analyses (process monitoring, control and optimisation) and requires one to select a measuring strategy, i.e., number and location of measurement points. This phase of data gathering usually impacts on inspection times and costs (via sample size) but it also affects the performance of the following tasks (process monitoring, control and optimisation). While most of the approaches for sampling design are specifically presented with reference to a target application (namely, monitoring, control or optimisation), this paper presents a general-purpose procedure, where the number and location of measurement points are selected in order to retain most of the information related to the feature under study. The procedure is based on principal component analysis and its application is shown with reference to a real case study concerning the left front window of a car. A different approach based on multidimensional scaling is further applied as validation tool, in order to show the effectiveness of the PCA solution