Which causal structures might support a quantum-classical gap?

A causal scenario is a graph that describes the cause and effect relationships between all relevant variables in an experiment. A scenario is deemed `not interesting' if there is no device-independent way to distinguish the predictions of classical physics from any generalised probabilistic theory (including quantum mechanics). Conversely, an interesting scenario is one in which there exists a gap between the predictions of different operational probabilistic theories, as occurs for example in Bell-type experiments. Henson, Lal and Pusey (HLP) recently proposed a sufficient condition for a causal scenario to not be interesting. In this paper we supplement their analysis with some new techniques and results. We first show that existing graphical techniques due to Evans can be used to confirm by inspection that many graphs are interesting without having to explicitly search for inequality violations. For three exceptional cases -- the graphs numbered 15,16,20 in HLP -- we show that there exist non-Shannon type entropic inequalities that imply these graphs are interesting. In doing so, we find that existing methods of entropic inequalities can be greatly enhanced by conditioning on the specific values of certain variables.Comment: 13 pages, 9 figures, 1 bicycle. Added an appendix showing that e-separation is strictly more general than the skeleton method. Added journal referenc

Classical causal models for Bell and Kochen-Specker inequality violations require fine-tuning

Nonlocality and contextuality are at the root of conceptual puzzles in quantum mechanics, and are key resources for quantum advantage in information-processing tasks. Bell nonlocality is best understood as the incompatibility between quantum correlations and the classical theory of causality, applied to relativistic causal structure. Contextuality, on the other hand, is on a more controversial foundation. In this work, I provide a common conceptual ground between nonlocality and contextuality as violations of classical causality. First, I show that Bell inequalities can be derived solely from the assumptions of no-signalling and no-fine-tuning of the causal model. This removes two extra assumptions from a recent result from Wood and Spekkens, and remarkably, does not require any assumption related to independence of measurement settings -- unlike all other derivations of Bell inequalities. I then introduce a formalism to represent contextuality scenarios within causal models and show that all classical causal models for violations of a Kochen-Specker inequality require fine-tuning. Thus the quantum violation of classical causality goes beyond the case of space-like separated systems, and manifests already in scenarios involving single systems.Comment: 9 pages, 14 figures. Modified title, discussion and presentatio

Treatment effect estimation with covariate measurement error

This paper investigates the effect that covariate measurement error has on a conventional treatment effect analysis built on an unconfoundedness restriction that embodies conditional independence restrictions in which there is conditioning on error free covariates. The approach uses small parameter asymptotic methods to obtain the approximate generic effects of measurement error. The approximations can be estimated using data on observed outcomes, the treatment indicator and error contaminated covariates providing an indication of the nature and size of measurement error effects. The approximations can be used in a sensitivity analysis to probe the potential effects of measurement error on the evaluation of treatment effects

"It from bit" and the quantum probability rule

I argue that, on the subjective Bayesian interpretation of probability, "it from bit" requires a generalization of probability theory. This does not get us all the way to the quantum probability rule because an extra constraint, known as noncontextuality, is required. I outline the prospects for a derivation of noncontextuality within this approach and argue that it requires a realist approach to physics, or "bit from it". I then explain why this does not conflict with "it from bit". This version of the essay includes an addendum responding to the open discussion that occurred on the FQXi website. It is otherwise identical to the version submitted to the contest.Comment: First prize winner of 2013 fqxi.org essay contest, "It from bit, or bit from it?". See http://fqxi.org/community/forum/topic/1938 and links therein. v1: LaTeX 10 pages v2: 14 pages. Updated for publication in Springer Frontiers Collection volum

Certainty in Heisenberg's uncertainty principle: Revisiting definitions for estimation errors and disturbance

We revisit the definitions of error and disturbance recently used in error-disturbance inequalities derived by Ozawa and others by expressing them in the reduced system space. The interpretation of the definitions as mean-squared deviations relies on an implicit assumption that is generally incompatible with the Bell-Kochen-Specker-Spekkens contextuality theorems, and which results in averaging the deviations over a non-positive-semidefinite joint quasiprobability distribution. For unbiased measurements, the error admits a concrete interpretation as the dispersion in the estimation of the mean induced by the measurement ambiguity. We demonstrate how to directly measure not only this dispersion but also every observable moment with the same experimental data, and thus demonstrate that perfect distributional estimations can have nonzero error according to this measure. We conclude that the inequalities using these definitions do not capture the spirit of Heisenberg's eponymous inequality, but do indicate a qualitatively different relationship between dispersion and disturbance that is appropriate for ensembles being probed by all outcomes of an apparatus. To reconnect with the discussion of Heisenberg, we suggest alternative definitions of error and disturbance that are intrinsic to a single apparatus outcome. These definitions naturally involve the retrodictive and interdictive states for that outcome, and produce complementarity and error-disturbance inequalities that have the same form as the traditional Heisenberg relation.Comment: 15 pages, 8 figures, published versio

Treatment effect estimation with covariate measurement error

This paper investigates the effect that covariate measurement error has on a conventional treatment effect analysis built on an unconfoundedness restriction that embodies conditional independence restrictions in which there is conditioning on error free covariates. The approach uses small parameter asymptotic methods to obtain the approximate generic effects of measurement error. The approximations can be estimated using data on observed outcomes, the treatment indicator and error contaminated covariates providing an indication of the nature and size of measurement error effects. The approximations can be used in a sensitivity analysis to probe the potential effects of measurement error on the evaluation of treatment effects.

Assumptions of IV Methods for Observational Epidemiology

Instrumental variable (IV) methods are becoming increasingly popular as they seem to offer the only viable way to overcome the problem of unobserved confounding in observational studies. However, some attention has to be paid to the details, as not all such methods target the same causal parameters and some rely on more restrictive parametric assumptions than others. We therefore discuss and contrast the most common IV approaches with relevance to typical applications in observational epidemiology. Further, we illustrate and compare the asymptotic bias of these IV estimators when underlying assumptions are violated in a numerical study. One of our conclusions is that all IV methods encounter problems in the presence of effect modification by unobserved confounders. Since this can never be ruled out for sure, we recommend that practical applications of IV estimators be accompanied routinely by a sensitivity analysis.Comment: Published in at http://dx.doi.org/10.1214/09-STS316 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org