Contextuality under weak assumptions

The presence of contextuality in quantum theory was first highlighted by Bell, Kochen and Specker, who discovered that for quantum systems of three or more dimensions, measurements could not be viewed as deterministically revealing pre-existing properties of the system. More precisely, no model can assign deterministic outcomes to the projectors of a quantum measurement in a way that depends only on the projector and not the context (the full set of projectors) in which it appeared, despite the fact that the Born rule probabilities associated with projectors are independent of the context. A more general, operational definition of contextuality introduced by Spekkens, which we will term "probabilistic contextuality", drops the assumption of determinism and allows for operations other than measurements to be considered contextual. Even two-dimensional quantum mechanics can be shown to be contextual under this generalised notion. Probabilistic noncontextuality represents the postulate that elements of an operational theory that cannot be distinguished from each other based on the statistics of arbitrarily many repeated experiments (they give rise to the same operational probabilities) are ontologically identical. In this paper, we introduce a framework that enables us to distinguish between different noncontextuality assumptions in terms of the relationships between the ontological representations of objects in the theory given a certain relation between their operational representations. This framework can be used to motivate and define a "possibilistic" analogue, encapsulating the idea that elements of an operational theory that cannot be unambiguously distinguished operationally can also not be unambiguously distinguished ontologically. We then prove that possibilistic noncontextuality is equivalent to an alternative notion of noncontextuality proposed by Hardy. Finally, we demonstrate that these weaker noncontextuality assumptions are sufficient to prove alternative versions of known "no-go" theorems that constrain ψ-epistemic models for quantum mechanics

Sudden collapse of a colloidal gel

Metastable gels formed by weakly attractive colloidal particles display a distinctive two-stage time-dependent settling behavior under their own weight. Initially a space-spanning network is formed that for a characteristic time, which we define as the lag time \taud, resists compaction. This solid-like behavior persists only for a limited time. Gels whose age \tw is greater than \taud yield and suddenly collapse. We use a combination of confocal microscopy, rheology and time-lapse video imaging to investigate both the process of sudden collapse and its microscopic origin in an refractive-index matched emulsion-polymer system. We show that the height $h$ of the gel in the early stages of collapse is well described by the surprisingly simple expression, h(\ts) = \h0 - A \ts^{3/2}, with \h0 the initial height and \ts = \tw-\taud the time counted from the instant where the gel first yields. We propose that this unexpected result arises because the colloidal network progressively builds up internal stress as a consequence of localized rearrangement events which leads ultimately to collapse as thermal equilibrium is re-established.Comment: 14 pages, 11 figures, final versio

Can lay-led walking programmes increase physical activity in middle aged adults? : a randomised controlled trial

Study objective: To compare health walks, a community based lay-led walking scheme versus advice only on physical activity and cardiovascular health status in middle aged adults. Design: Randomised controlled trial with one year follow up. Physical activity was measured by questionnaire. Other measures included attitudes to exercise, body mass index, cholesterol, aerobic capacity, and blood pressure. Setting: Primary care and community. Participants: 260 men and women aged 40–70 years, taking less than 120 minutes of moderate intensity activity per week. Main results: Seventy three per cent of people completed the trial. Of these, the proportion increasing their activity above 120 minutes of moderate intensity activity per week was 22.6% in the advice only and 35.7% in the health walks group at 12 months (between group difference =13% (95% CI 0.003% to 25.9%) p=0.05). Intention to treat analysis, using the last known value for missing cases, demonstrated smaller differences between the groups (between group difference =6% (95% CI -5% to 16.4%)) with the trend in favour of health walks. There were improvements in the total time spent and number of occasions of moderate intensity activity, and aerobic capacity, but no statistically significant differences between the groups. Other cardiovascular risk factors remained unchanged. Conclusions: There were no significant between group differences in self reported physical activity at 12 month follow up when the analysis was by intention to treat. In people who completed the trial, health walks was more effective than giving advice only in increasing moderate intensity activity above 120 minutes per week

Structural investigations of phosphorus-nitrogen compounds. 7. Relationships between physical properties, electron densities, reaction mechanisms and hydrogen-bonding motifs of N3P3Cl(6-n)(NHBut)(n) derivatives

A series of compounds of the N3P3Cl(6-n)(NHBut)n family (where n = 0, 1, 2, 4 and 6) are presented and their molecular parameters are related to trends in physical properties, which provides insight into a potential reaction mechanism for nucleophilic substitution. The crystal structures of N3P3Cl5(NHBut) and N3P3Cl2(NHBut)4 have been determined at 120K and those of N3P3Cl6 and N3P3Cl4(NHBut)2 have been re-determined at 120K. These are compared with the known structure of N3P3(NHBut)6 studied at 150K. Trends in molecular parameters (phosphazene ring, P-Cl & P-N(HBut) distances, PCl2 angles and endo- and exo-cyclic phosphazene ring parameters) across the series are observed. Hydrogen-bonding motifs are identified, characterised and compared. Both the molecular and hydrogen bonding parameters are related to the electron distribution in bonds and the derived basicities of the cyclophosphazene series of compounds. These findings provide evidence for a proposed mechanism for nucleophilic substitution at a phosphorus site bearing a PCl(NHBut) moiety

Orientation and symmetry control of inverse sphere magnetic nanoarrays by guided self-assembly

Inverse sphere shaped Ni arrays were fabricated by electrodeposition on Si through the guided self-assembly of polystyrene latex spheres in Si/SiO2 patterns. It is shown that the size commensurability of the etched tracks is critical for the long range ordering of the spheres. Moreover, noncommensurate guiding results in the reproducible periodic triangular distortion of the close packed self-assembly. Magnetoresistance measurements on the Ni arrays were performed showing room temperature anisotropic magnetoresistance of 0.85%. These results are promising for self-assembled patterned storage media and magnetoresistance devices

Characterization of a qubit Hamiltonian using adaptive measurements in a fixed basis

We investigate schemes for Hamiltonian parameter estimation of a two-level system using repeated measurements in a fixed basis. The simplest (Fourier based) schemes yield an estimate with a mean square error (MSE) that decreases at best as a power law ~N^{-2} in the number of measurements N. By contrast, we present numerical simulations indicating that an adaptive Bayesian algorithm, where the time between measurements can be adjusted based on prior measurement results, yields a MSE which appears to scale close to \exp(-0.3 N). That is, measurements in a single fixed basis are sufficient to achieve exponential scaling in N.Comment: 5 pages, 3 figures, 1 table. Published versio

Unitary transformations for testing Bell inequalities

It is shown that optical experimental tests of Bell inequality violations can be described by SU(1,1) transformations of the vacuum state, followed by photon coincidence detections. The set of all possible tests are described by various SU(1,1) subgroups of Sp(8,$\Bbb R$). In addition to establishing a common formalism for physically distinct Bell inequality tests, the similarities and differences of post--selected tests of Bell inequality violations are also made clear. A consequence of this analysis is that Bell inequality tests are performed on a very general version of SU(1,1) coherent states, and the theoretical violation of the Bell inequality by coincidence detection is calculated and discussed. This group theoretical approach to Bell states is relevant to Bell state measurements, which are performed, for example, in quantum teleportation.Comment: 3 figure

Why we need a public understanding of social science

Copyright © The Author(s) 2023. Who is licensed to make knowledge claims about society? A more diffuse group of individuals are afforded the status of legitimate speakers on society in the public sphere than is the case when the questions relate to the expertise of the natural sciences. We draw on the concept of the ‘locus of legitimate interpretation’ and the sensibilities of Collins and Evans’ Studies of Expertise and Experience programme to help make sense of these issues. The social sciences are not the natural sciences, and one key difference is their relationship with publics. The social sciences are intrinsically entangled, at both the level of the research question and the research subject/object, with public knowledge, the knowledges of publics and public interests. We therefore outline what these differences might mean for a serious, distinct and purposive Public Understanding of Social Science programme and how this differs from current work in the Public Understanding of Science.The author(s) received no financial support for the research, authorship and/or publication of this article

Multiple-copy state discrimination: Thinking globally, acting locally

We theoretically investigate schemes to discriminate between two nonorthogonal quantum states given multiple copies. We consider a number of state discrimination schemes as applied to nonorthogonal, mixed states of a qubit. In particular, we examine the difference that local and global optimization of local measurements makes to the probability of obtaining an erroneous result, in the regime of finite numbers of copies $N$, and in the asymptotic limit as $N \rightarrow \infty$. Five schemes are considered: optimal collective measurements over all copies, locally optimal local measurements in a fixed single-qubit measurement basis, globally optimal fixed local measurements, locally optimal adaptive local measurements, and globally optimal adaptive local measurements. Here, adaptive measurements are those for which the measurement basis can depend on prior measurement results. For each of these measurement schemes we determine the probability of error (for finite $N$) and scaling of this error in the asymptotic limit. In the asymptotic limit, adaptive schemes have no advantage over the optimal fixed local scheme, and except for states with less than 2% mixture, the most naive scheme (locally optimal fixed local measurements) is as good as any noncollective scheme. For finite $N$, however, the most sophisticated local scheme (globally optimal adaptive local measurements) is better than any other noncollective scheme, for any degree of mixture.Comment: 11 pages, 14 figure

A comparison of single-cycle versus multiple-cycle proof testing strategies

An evaluation of single-cycle and multiple-cycle proof testing (MCPT) strategies for SSME components is described. Data for initial sizes and shapes of actual SSME hardware defects are analyzed statistically. Closed-form estimates of the J-integral for surface flaws are derived with a modified reference stress method. The results of load- and displacement-controlled stable crack growth tests on thin IN-718 plates with deep surface flaws are summarized. A J-resistance curve for the surface-cracked configuration is developed and compared with data from thick compact tension specimens. The potential for further crack growth during large unload/reload cycles is discussed, highlighting conflicting data in the literature. A simple model for ductile crack growth during MCPT based on the J-resistance curve is used to study the potential effects of key variables. The projected changes in the crack size distribution during MCPT depend on the interactions between several key parameters, including the number of proof cycles, the nature of the resistance curve, the initial crack size distribution, the component boundary conditions (load vs. displacement control), and the magnitude of the applied load or displacement. The relative advantages of single-cycle and multiple-cycle proof testing appear to be specific, therefore, to individual component geometry, material, and loading