Observers can always generate nonlocal correlations without aligning measurements by covering all their bases

Quantum theory allows for correlations between the outcomes of distant measurements that are inconsistent with any locally causal theory, as demonstrated by the violation of a Bell inequality. Typical demonstrations of these correlations require careful alignment between the measurements, which requires distant parties to share a reference frame. Here, we prove, following a numerical observation by Shadbolt et al., that if two parties share a Bell state and each party randomly chooses three orthogonal measurements, then the parties will always violate a Bell inequality. Furthermore, we prove that this probability is highly robust against local depolarizing noise, in that small levels of noise only decrease the probability of violating a Bell inequality by a small amount. We also show that generalizing to N parties increases the robustness against noise. These results improve on previous ones that only allowed a high probability of violating a Bell inequality for large numbers of parties.Comment: 4 pages, 2 figures. v2: updated reference. v3: published versio

Difficulty of distinguishing product states locally

Non-locality without entanglement is a rather counter-intuitive phenomenon in which information may be encoded entirely in product (unentangled) states of composite quantum systems in such a way that local measurement of the subsystems is not enough for optimal decoding. For simple examples of pure product states, the gap in performance is known to be rather small when arbitrary local strategies are allowed. Here we restrict to local strategies readily achievable with current technology; those requiring neither a quantum memory nor joint operations. We show that, even for measurements on pure product states there can be a large gap between such strategies and theoretically optimal performance. Thus even in the absence of entanglement physically realizable local strategies can be far from optimal for extracting quantum information.Comment: 5 pages, 1 figur

Generating nonclassical correlations without fully aligning measurements

We investigate the scenario where spatially separated parties perform measurements in randomly chosen bases on an N-partite Greenberger-Horne-Zeilinger state. We show that without any alignment of the measurements, the observers will obtain correlations that violate a Bell inequality with a probability that rapidly approaches 1 as N increases and that this probability is robust against noise. We also prove that restricting these randomly chosen measurements to a plane perpendicular to a common direction will always generate correlations that violate some Bell inequality. Specifically, if each observer chooses their two measurements to be locally orthogonal, then the N observers will violate one of two Bell inequalities by an amount that increases exponentially with N. These results are also robust against noise and perturbations of each observer's reference direction from the common direction.Comment: v2: Essentially published version (with typos fixed, results updated in Table 2 and Figure 4 replaced); v1: 16 pages, 5 figures, 2 tables, comments welcom

Joint measurements and Bell inequalities

Joint quantum measurements of non-commuting observables are possible, if one accepts an increase in the measured variances. A necessary condition for a joint measurement to be possible is that a joint probability distribution exists for the measurement. This fact suggests that there may be a link with Bell inequalities, as these will be satisfied if and only if a joint probability distribution for all involved observables exists. We investigate the connections between Bell inequalities and conditions for joint quantum measurements to be possible. Mermin's inequality for the three-particle Greenberger-Horne-Zeilinger state turns out to be equivalent to the condition for a joint measurement on two out of the three quantum systems to exist. Gisin's Bell inequality for three co-planar measurement directions, meanwhile, is shown to be less strict than the condition for the corresponding joint measurement

Integrated stratigraphy of the Kimmeridge Clay Formation (Upper Jurassic) based on exposures and boreholes in south Dorset, UK

For the purposes of a high-resolution multi-disciplinary study of the Upper Jurassic Kimmeridge Clay Formation, two boreholes were drilled at Swanworth Quarry and one at Metherhills, south Dorset, UK. Together, the cores represent the first complete section through the entire formation close to the type section. We present graphic logs that record the stratigraphy of the cores, and outline the complementary geophysical and analytical data sets (gamma ray, magnetic susceptibility, total organic carbon, carbonate, [delta]13Corg). Of particular note are the new borehole data from the lowermost part of the formation which does not crop out in the type area. Detailed logs are available for download from the Kimmeridge Drilling Project web-site at http://kimmeridge.earth.ox.ac.uk/. Of further interest is a mid-eudoxus Zone positive shift in the [delta]13Corg record, a feature that is also registered in Tethyan carbonate successions, suggesting that it is a regional event and may therefore be useful for correlation. The lithostratigraphy of the cores has been precisely correlated with the nearby cliff section, which has also been examined and re-described. Magnetic-susceptibility and spectral gamma-ray measurements were made at a regular spacing through the succession, and facilitate core-to-exposure correlation. The strata of the exposure and core have been subdivided into four main mudrock lithological types: (a) medium-dark–dark-grey marl; (b) medium-dark–dark grey–greenish black shale; (c) dark-grey–olive-black laminated shale; (d) greyish-black–brownish-black mudstone. The sections also contain subordinate amounts of siltstone, limestone and dolostone. Comparison of the type section with the cores reveals slight lithological variation and notable thickness differences between the coeval strata. The proximity of the boreholes and different parts of the type section to the Purbeck–Isle of Wight Disturbance is proposed as a likely control on the thickness changes

Applications of three-dimensional printing in ophthalmology

Three-dimensional (3D) printing is increasingly used to produce customised objects and is a promising alternative to traditional manufacturing methods in diverse fields, such as dentistry and orthopaedics. Already in use in other medical specialities, adoption in ophthalmology has been limited to date. This review aims to provide an overview of 3D printing technology with respect to current and potential applications in ophthalmic practice. Medline, Embase and internet search were performed with "3D printing", "ophthalmology", "dentistry", "orthopaedics" and their synonyms used as main search terms. In addition, search terms related to clinical applications such as "surgery" and "implant" were employed. 3D printing has multiple applications in ophthalmology, including in diagnosis, surgery, prosthetics, medications and medical education. Within the past decade, researchers have produced 3D printed models of objects such as implants, prostheses, anatomical models and surgical simulators. Further development is necessary to generate optimal biomaterials for various applications, and the quality and long-term performance of 3D models needs to be validated

The simplest demonstrations of quantum nonlocality

We investigate the complexity cost of demonstrating the key types of nonclassical correlations-Bell inequality violation, Einstein, Podolsky, Rosen (EPR)-steering, and entanglement-with independent agents, theoretically and in a photonic experiment. We show that the complexity cost exhibits a hierarchy among these three tasks, mirroring the recently discovered hierarchy for how robust they are to noise. For Bell inequality violations, the simplest test is the well-known Clauser-Horne-Shimony-Holt test, but for EPR-steering and entanglement the tests that involve the fewest number of detection patterns require nonprojective measurements. The simplest EPR-steering test requires a choice of projective measurement for one agent and a single nonprojective measurement for the other, while the simplest entanglement test uses just a single nonprojective measurement for each agent. In both of these cases, we derive our inequalities using the concept of circular two-designs. This leads to the interesting feature that in our photonic demonstrations, the correlation of interest is independent of the angle between the linear polarizers used by the two parties, which thus require no alignment

Joint measurements of spin, operational locality and uncertainty

Joint, or simultaneous, measurements of non-commuting observables are possible within quantum mechanics, if one accepts an increase in the variances of the jointly measured observables. In this paper, we discuss joint measurements of a spin 1/2 particle along any two directions. Starting from an operational locality principle, it is shown how to obtain a bound on how sharp the joint measurement can be. We give a direct interpretation of this bound in terms of an uncertainty relation.Comment: Accepted for publication in Phys. Rev.

Demonstrating superior discrimination of locally prepared states using nonlocal measurements

We experimentally demonstrate the superior discrimination of separated, unentangled two-qubit correlated states using nonlocal measurements, when compared with measurements based on local operations and classical communications. When predicted theoretically, this phenomenon was dubbed quantum nonlocality without entanglement. We characterize the performance of the nonlocal, or joint, measurement with a payoff function, for which we measure 0.72 +/- 0.02, compared with the maximum locally achievable value of 2/3 and the overall optimal value of 0.75

What Type of Person Would Be Willing to Fly with Children? A Multi-Model Analysis

The purpose of this study was to assess the type of person who would be willing to fly with children in various scenarios. A quantitative methodology and a non-experimental research approach were used in this study. A two-stage approach created a regression equation then assessed model fit. Six hundred and twenty participants were recruited for the study. The dataset was split randomly into two groups to facilitate the two-stage approach, resulting in 310 participants per stage. The study used 14 possible predictors to determine willingness to fly in five different scenarios. Five models were created and found between two and four predictors of passengers who were willing to fly with children in various scenarios. We were able to explain between 14.3% and 18.6% of the variance. All five equations were assessed for model fit and found to support a good model fit. Many aviation studies have examined willingness to fly in various scenarios; however, no research specific to the type of person who would be willing to fly with children has been explored. This study aims to fill that gap by exploring the type of person who would fly with children in five different scenarios