Assumption Of Measurement Independence Research Articles

Superdeterminism without Conspiracy

Superdeterminism—where the Measurement Independence assumption in Bell’s Theorem is violated—is frequently assumed to imply implausibly conspiratorial correlations between properties λ of particles being measured and measurement settings x and y. But it does not have to be so: a superdeterministic but non-conspiratorial locally causal model is developed where each pair of entangled particles has unique λ. The model is based on a specific but arbitrarily fine discretisation of complex Hilbert space, where λ defines the information, over and above the freely chosen nominal settings x and y, which fixes the exact measurement settings X and Y of a run of a Bell experiment. Pearlean interventions, needed to assess whether x and y are Bell-type free variables, are shown to be inconsistent with rational-number constraints on the discretised Hilbert states. These constraints limit the post-hoc freedom to vary x keeping λ and y fixed but disappear with any coarse-graining of λ, X, and Y, rendering so-called drug-trial conspiracies irrelevant. Points in the discretised space can be realised as ensembles of symbolically labelled deterministic trajectories on an ‘all-at-once’ fractal attractor. It is shown how quantum mechanics might be ‘gloriously explained and derived’ as the singular continuum limit of the discretisation of Hilbert space. It is argued that the real message behind Bell’s Theorem has less to do with locality, realism, or freedom to choose, and more to do with the need to develop more explicitly holistic theories when attempting to synthesise quantum and gravitational physics.

Exponential Mixture Density Based Approximation to Posterior Cramér-Rao Lower Bound for Distributed Target Tracking

The posterior Cramr-Rao lower bound (PCRLB) and a number of its extensions including the unconditional PCRLB (U-PCRLB) and the conditional PCRLB (C-PCRLB) have been widely studied in multi-sensor target tracking (MSTT). Previous MSTT works assume that the measurements are conditionally independent, which is often not the case in practice. When the correlations of the measurements are unknown, the standard Bayes update and PCRLB computations cannot be performed. Inspired by geometric average (GA) fusion that implements data fusion with unknown data correlations by employing exponential mixture density (EMD) to compute the global posterior, EMD-based approximations to U-PCRLB and C-PCRLB are derived in this paper for two classic distributed fusion architectures, namely the hierarchical and consensus architectures. The PCRLB can be decomposed into two parts, one coming from the prior information and the other from the information contained in the data. The data information part of PCRLB is approximated via EMD-based posterior, leading to the approximation of the PCRLB. We present a sequential Monte Carlo solution to recursively compute the proposed approximation to the PCRLB for nonlinear non-Gaussian estimation problems. Numerical simulations are provided to show that the proposed approximation to the bound on the estimation mean square error (MSE) is tighter compared to the existing bounds based on likelihood fusion obtained under the measurement independence assumption.

Effects of measurement dependence on 1-parameter family of Bell tests

Most quantum information tasks based on Bell tests rely on the assumption of measurement independence. However, it is difficult to ensure that the assumption of measurement independence is always met in experimental operations, so it is crucial to explore the effects of relaxing this assumption on Bell tests. In this paper, we discuss the effects of relaxing the assumption of measurement independence on 1-parameter family of Bell (1-PFB) tests. For both general and factorizable input distributions, we establish the relationship among measurement dependence, guessing probability, and the maximum value of 1-PFB correlation function that Eve can fake. The deterministic strategy when Eve fakes the maximum value is also given. We compare the unknown information rate of Chain inequality and 1-PFB inequality and find that there exists a parameter range in which it is more difficult for Eve to fake the maximum quantum violation in 1-PFB inequality than in Chain inequality.

Measurement-dependence cost for Bell nonlocality: Causal versus retrocausal models

Device independent protocols based on Bell nonlocality, such as quantum key distribution and randomness generation, must ensure no adversary can have prior knowledge of the measurement outcomes. This requires a measurement independence assumption: that the choice of measurement is uncorrelated with any other underlying variables that influence the measurement outcomes. Conversely, relaxing measurement independence allows for a fully `causal' simulation of Bell nonlocality. We construct the most efficient such simulation, as measured by the mutual information between the underlying variables and the measurement settings, for the Clauser-Horne-Shimony-Holt (CHSH) scenario, and find that the maximal quantum violation requires a mutual information of just $\sim 0.080$ bits. Any physical device built to implement this simulation allows an adversary to have full knowledge of a cryptographic key or `random' numbers generated by a device independent protocol based on violation of the CHSH inequality. We also show that a previous model for the CHSH scenario, requiring only $\sim 0.046$ bits to simulate the maximal quantum violation, corresponds to the most efficient `retrocausal' simulation, in which future measurement settings necessarily influence earlier source variables. This may be viewed either as an unphysical limitation of the prior model, or as an argument for retrocausality on the grounds of its greater efficiency. Causal and retrocausal models are also discussed for maximally entangled two-qubit states, as well as superdeterministic, one-sided and zigzag causal models.

Relaxed Bell inequalities with arbitrary measurement dependence for each observer

Bell's inequality was originally derived under the assumption that experimenters are free to select detector settings independently of any local "hidden variables" that might affect the outcomes of measurements on entangled particles. This assumption has come to be known as "measurement independence" (also referred to as "freedom of choice" or "settings independence"). For a two-setting, two-outcome Bell test, we derive modified Bell inequalities that relax measurement independence, for either or both observers, while remaining locally causal. We describe the loss of measurement independence for each observer using the parameters $M_1$ and $M_2$, as defined by Hall in 2010, and also by a more complete description that adds two new parameters, which we call $\hat{M}_1$ and $\hat{M}_2$, deriving a modified Bell inequality for each description. These "relaxed" inequalities subsume those considered in previous work as special cases, and quantify how much the assumption of measurement independence needs to be relaxed in order for a locally causal model to produce a given violation of the standard Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality. We show that both relaxed Bell inequalities are tight bounds on the CHSH parameter by constructing locally causal models that saturate them. For any given Bell inequality violation, the new two-parameter and four-parameter models each require significantly less mutual information between the hidden variables and measurement settings than previous models. We conjecture that the new models, with optimal parameters, require the minimum possible mutual information for a given Bell violation. We further argue that, contrary to various claims in the literature, relaxing freedom of choice need not imply superdeterminism.

Measurement dependent locality

The demonstration and use of Bell-nonlocality, a concept that is fundamentally striking and is at the core of applications in device independent quantum information processing, relies heavily on the assumption of measurement independence, also called the assumption of free choice. The latter cannot be verified or guaranteed. In this paper, we consider a relaxation of the measurement independence assumption. We briefly review the results of Pütz et al (2014 Phys. Rev. Lett. 113 190402), which show that with our relaxation, the set of so-called measurement dependent local (MDL) correlations is a polytope, i.e. it can be fully described using a finite set of linear inequalities. Here we analyze this polytope, first in the simplest case of two parties with binary inputs and outputs, for which we give a full characterization. We show that partially entangled states are preferable to the maximally entangled state when dealing with measurement dependence in this scenario. We further present a method which transforms any Bell-inequality into an MDL inequality and give valid inequalities for the case of arbitrary number of parties as well as one for arbitrary number of inputs. We introduce the assumption of independent sources in the measurement dependence scenario and give a full analysis for the bipartite scenario with binary inputs and outputs. Finally, we establish a link between measurement dependence and another strong hindrance in certifying nonlocal correlations: nondetection events.

Demonstration of Quantum Nonlocality in the Presence of Measurement Dependence.

Quantum nonlocality stands as a resource for device independent quantum information processing (DIQIP), such as, for instance, device independent quantum key distribution. We investigate, experimentally, the assumption of limited measurement dependence, i.e., that the measurement settings used in Bell inequality tests or DIQIP are partially influenced by the source of entangled particle and/or by an adversary. Using a recently derived Bell-like inequality [G. Pütz, Phys. Rev. Lett. 113, 190402 (2014)] and a 99% fidelity source of partially entangled polarization photonic qubits, we obtain a clear violation of the inequality, excluding a much larger range of measurement dependent local models than would be possible with an adapted Clauser-Horne-Shimony-Holt (CHSH) inequality. It is therefore shown that the measurement independence assumption can be widely relaxed while still demonstrating quantum nonlocality.

Elevated percentage of HLA-DR+ and ICAM-1+ conjunctival epithelial cells in active Graves’ orbitopathy

Dear Editor, We readwith interest the article by Pawlowski et al. describing an elevated percentage of HLA-DR and ICAM-1 conjunctival epithelial cells in active Graves’ orbitopathy [1]. Although the study is mostly well designed and analyzed, we have the following questions and comments. The authors concluded that the percentage of HLA-DR and ICAM-1 conjunctival epithelial cells in patients with active Graves’ orbitopathy (GO) may serve as a topical inflammation marker in GO (from the results in Table 2 and Fig. 2); their data showed differences between the active GO vs. Graves’ disease (GD) without active GO and vs. normal control, respectively, using two separate Mann–Whitney U tests. Their conclusions could be more convincing if they were obtained by a Kruskal-Wallis test with Dunn’s nonparametric multiple comparisons or with a method (e.g., Bonferroni adjustment) to avoid the increase of the statistical significance level due to multiple hypothesis tests [2, 3]. Furthermore, data obtained from fifteen eyes of ten healthy volunteers (normal control) do not satisfy the assumption of the Mann–Whitney test that the observations in a sample are independent. In this study, violation of the measurement independence assumption principle partly occurred; all observations both in active GO and GD without active GO are independent, while two-thirds of the measurements in normal controls are dependent. Thus we recommend that only ten observations (one eye per person) should be used in the statistical test. An excellent reference for the statistical methods regarding the dependence of observations in ophthalmology was given by Armstrong [4].

Alternative experimental protocol to demonstrate the Pusey-Barrett-Rudolph theorem

Pusey, Barrett and Rudolph (PBR) have recently proven an important new theorem in the foundations of quantum mechanics. Here we propose alternative experimental protocols which lead to the PBR result for a special case and a weaker PBR-like result generally. Alternative experimental protocols support the assumption of measurement independence required for the PBR theorem.

Local Deterministic Model of Singlet State Correlations Based on Relaxing Measurement Independence

The derivation of Bell inequalities requires an assumption of measurement independence, related to the amount of free will experimenters have in choosing measurement settings. Violation of these inequalities by singlet state correlations brings this assumption into question. A simple measure of the degree of measurement independence is defined for correlation models, and it is shown that all spin correlations of a singlet state can be modeled via giving up just 14% of measurement independence. The underlying model is deterministic and no signaling. It may thus be favorably compared with other underlying models of the singlet state, which require maximum indeterminism or maximum signaling. A local deterministic model is also given that achieves the maximum possible violation of the well-known Bell-Clauser-Horne-Shimony-Holt inequality, at a cost of only 1/3 of measurement independence.

Correlation and covariance of satellite scatterometer measurements

Capable scatterometer designs have been developed that seek improved resolution through the use of higher pulse sampling rates. The high sampling rates bring the traditional scatterometry assumption of measurement independence into question. This paper uses fundamental scattering theory to derive general expressions for correlation and covariance between scatterometer measurements and provides practical analysis using current and future instruments as examples. The paper derives expressions for the measurement variance parameter K/sub p/ when measurement correlation due to Rayleigh fading effects is present and relates K/sub p/ to the statistics of multiple pulse measurements. A function of the transmit signal modulation and receive processing, the measurement correlation is zero for nonoverlapping measurements but can become significant for overlapping measurements at high pulse sampling rates. The paper discusses the effects of correlation on the accuracy of scatterometer measurements and evaluates tradeoffs between spatial overlap, levels of additive noise, and measurement precision.

QUESTIONNAIRE VALIDATION BY CONFIRMATORY FACTOR ANALYSIS: AN IMPROVEMENT OVER MULTITRAIT‐MULTIMETHOD MATRICES*

ABSTRACTThe Campbell and Fiske criteria for assessing the construct validity of multitrait‐multimethod (MTMM) matrices has had a long history of use. While various statistical techniques, including ANOVA, have attempted to provide rigor to the MTMM matrix design, numerous problems still remain unsolved. Part of the problem in using an MTMM matrix is the assumption of measurement independence. This study attempts to illustrate the misleading inferences that often occur from MTMM analysis when method variance overlap is not accurately assessed. Three questionnaires were designed that were not method independent. Traditional procedures for assessing MTMM matrices suggested the three scaling formats used were not burdened with unusual method variance. A reanalysis of the MTMM matrix employing a Confirmatory Factor Analysis technique illustrated that method variance was a problem. Finally, the need for studies that concentrate on the nature of method variance, its causes and effects, is discussed.