An operational link between MUBs and SICs

We exhibit an operational connection between mutually unbiased bases and symmetric infomationally complete positive operator-valued measures. Assuming that the latter exists, we show that there is a strong link between these two structures in all prime power dimensions. We also demonstrate that a similar link cannot exists in dimension 6.Comment: 17 pages, 2 figure

From Incompatibility to Optimal Joint Measurability in Quantum Mechanics

This thesis is concerned with several topics related to concept of incompatibility of quan- tum observables. The operational description of quantum theory is given, in which incom- patibility is expressed in terms of joint measurability. A connection between symmetric informationally complete positive operator-valued measures and mutually unbiased bases is given, and examples of this connection holding based on investigations in Mathematica are presented. An extension of the Arthurs-Kelly measurement model is then given, where the measured observable is calculated, thereby generalising the results given previously in the literature. It is shown that in the case of prior correlations between measurement probes there exists the possibility that a measurement of both probes leads to marginal observables with smaller statistical spread than if measurements are performed on the individual probes. This concept is then highlighted by considering two probe states that allow for this reduction in spread, and the required conditions for success are given. Fi- nally, error-error relations for incompatible dichotomic qubit observables are considered in the case of state-dependent and independent error measures. Quantities that arise in the state-independent measures case, which were previously presented geometrically, have been given operational meaning, and optimal approximating schemes in both cases are compared. Limitations regarding the state-dependent optimal approximations, and experimental work built upon this construction are also discussed

Quantum state discrimination via repeated measurements and the rule of three

The task of state discrimination for a set of mutually orthogonal pure states is trivial if one has access to the corresponding sharp (projection-valued) measurement, but what if we are restricted to an unsharp measurement? Given that any realistic measurement device will be subject to some noise, such a problem is worth considering. In this paper, we consider minimum error state discrimination for mutually orthogonal states with a noisy measurement. We show that by considering repetitions of commutative Lüders measurements on the same system we are able to increase the probability of successfully distinguishing states. In the case of binary Lüders measurements, we provide a full characterisation of the success probabilities for any number of repetitions. This leads us to identify a ‘rule of three’, where no change in probability is obtained from a second measurement but there is noticeable improvement after a third. We also provide partial results for N-valued commutative measurements where the rule of three remains, but the general pattern present in binary measurements is no longer satisfied

BJC News

Vol.1, No.1 - September 27, 1956. First issue of the Boone Junior College News.https://openspace.dmacc.edu/banner_news/1010/thumbnail.jp

All quantum resources provide an advantage in exclusion tasks

A key ingredient in quantum resource theories is a notion of measure. Such as a measure should have a number of fundamental properties, and desirably also a clear operational meaning. Here we show that a natural measure known as the convex weight, which quantifies the resource cost of a quantum device, has all the desired properties. In particular, the convex weight of any quantum resource corresponds exactly to the relative advantage it offers in an exclusion task. After presenting the general result, we show how the construction works for state assemblages, sets of measurements and sets of transformations. Moreover, in order to bound the convex weight analytically, we give a complete characterisation of the convex components and corresponding weights of such devices.Comment: 8 pages, comments are welcom

Detector-Free Optimization of Traffic Signal Offsets with Connected Vehicle Data

It has recently been shown that signal offset optimization is feasible using vehicle trajectory data at low levels of market penetration. This study performs offset optimization on two corridors using this type ofdata. Six weeks oftrajectory splines were processed for two corridors including 25 signalized intersections, in order to create vehicle arrival profiles, using a proposed procedure called virtual detection. After processing and filtering the data, penetration rates between 0.09-0.80% were observed, varying by approach. The arrival profiles were statistically compared against those measured with physical detectors, with the majority of the approaches showing statistically significant goodness-of-fit at a 90% confidence level. Finally, the virtual detection arrival profiles were used to optimize offsets, and compared against a solution derived from physical detector arrival profiles. The results demonstrate that virtual detection can produce good quality offsets with current market penetration rates of probe data. The study also includes a sensitivity analysis to the sample period, which shows that two weeks of data may be sufficient for data collection at current penetration rates