35 research outputs found
Nonlocality free wirings and the distinguishability between Bell boxes
Bell nonlocality can be formulated in terms of a resource theory with local-hidden variable models as resourceless objects. Two such theories are known, one built upon local operations assisted by shared randomness (LOSRs) and the other one allowing, in addition, for prior-to-input classical communication. We show that prior communication, although unable to create nonlocality, leads to wirings not only beyond LOSRs but also not contained in a much broader class of (nonlocality-generating) global wirings. Technically, this is shown by proving that it can improve the statistical distinguishability between Bell correlations optimized over all fixed measurement choices. This has implications in nonlocality quantification, and leads us to a natural universal definition of Bell nonlocality measures. To end up with, we also consider the statistical strength of nonlocality proofs. We point out some issues of its standard definition in the resource-theoretic operational framework, and suggest simple fixes for them. Our findings reveal nontrivial features of the geometry of the set of wirings and may have implications in the operational distinguishability of nonlocal behaviors
Noncontextual wirings
Contextuality is a fundamental feature of quantum theory and is necessary for
quantum computation and communication. Serious steps have therefore been taken
towards a formal framework for contextuality as an operational resource.
However, the most important component for a resource theory - a concrete,
explicit form for the free operations of contextuality - was still missing.
Here we provide such a component by introducing noncontextual wirings: a
physically-motivated class of contextuality-free operations with a friendly
parametrization. We characterize them completely for the general case of
black-box measurement devices with arbitrarily many inputs and outputs. As
applications, we show that the relative entropy of contextuality is a
contextuality monotone and that maximally contextual boxes that serve as
contextuality bits exist for a broad class of scenarios. Our results complete a
unified resource-theoretic framework for contextuality and Bell nonlocality
A proof of Bell's inequality in quantum mechanics using causal interactions
We give a simple proof of Bell's inequality in quantum mechanics which, in
conjunction with experiments, demonstrates that the local hidden variables
assumption is false. The proof sheds light on relationships between the notion
of causal interaction and interference between particles.Comment: http://biostats.bepress.com/cobra/art8
Statistics, Causality and Bell's Theorem
Bell's [Physics 1 (1964) 195-200] theorem is popularly supposed to establish
the nonlocality of quantum physics. Violation of Bell's inequality in
experiments such as that of Aspect, Dalibard and Roger [Phys. Rev. Lett. 49
(1982) 1804-1807] provides empirical proof of nonlocality in the real world.
This paper reviews recent work on Bell's theorem, linking it to issues in
causality as understood by statisticians. The paper starts with a proof of a
strong, finite sample, version of Bell's inequality and thereby also of Bell's
theorem, which states that quantum theory is incompatible with the conjunction
of three formerly uncontroversial physical principles, here referred to as
locality, realism and freedom. Locality is the principle that the direction of
causality matches the direction of time, and that causal influences need time
to propagate spatially. Realism and freedom are directly connected to
statistical thinking on causality: they relate to counterfactual reasoning, and
to randomisation, respectively. Experimental loopholes in state-of-the-art Bell
type experiments are related to statistical issues of post-selection in
observational studies, and the missing at random assumption. They can be
avoided by properly matching the statistical analysis to the actual
experimental design, instead of by making untestable assumptions of
independence between observed and unobserved variables. Methodological and
statistical issues in the design of quantum Randi challenges (QRC) are
discussed. The paper argues that Bell's theorem (and its experimental
confirmation) should lead us to relinquish not locality, but realism.Comment: Published in at http://dx.doi.org/10.1214/14-STS490 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org