Two central concepts of quantum mechanics are Heisenberg's uncertainty principle and a subtle form of nonlocality that Einstein famously called "spooky action at a distance." These two fundamental features have thus far been distinct concepts. We show that they are inextricably and quantitatively linked: Quantum mechanics cannot be more nonlocal with measurements that respect the uncertainty principle. In fact, the link between uncertainty and nonlocality holds for all physical theories. More specifically, the degree of nonlocality of any theory is determined by two factors: the strength of the uncertainty principle and the strength of a property called "steering," which determines which states can be prepared at one location given a measurement at another.

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The uncertainty principle determines the nonlocality of quantum mechanics.

In/Proceedings of the 15th IEEE International Conference on the Engineering of Complex Computer Systems/ (ICECCS 2010), Oxford

Resource theories can be used to formalize the quantification and manipulation of resources in quantum information processing such as entanglement, asymmetry and coherence of quantum states, and incompatibility of quantum measurements. Given a certain state or measurement, one can ask whether there is a task in which it performs better than any resourceless state or measurement. Using conic programming, we prove that any general robustness measure (with respect to a convex set of free states or measurements) can be seen as a quantifier of such outperformance in some discrimination task. We apply the technique to various examples, e.g., joint measurability, positive operator valued measures simulable by projective measurements, and state assemblages preparable with a given Schmidt number.

Quantifying Quantum Resources with Conic Programming.

The blazar 3C 454.3 was revealed by the Fermi Gamma-ray Space Telescope to be in an exceptionally high flux state in 2008 July. Accordingly, we performed a multiwavelength monitoring campaign from 2008 August through December on this blazar using infrared (IR) and optical observations from the Small and Moderate Aperture Research Telescope System telescopes, optical, ultraviolet (UV), and X-ray data from the Swift satellite, and public-release gamma-ray data from Fermi. We find an excellent correlation between the IR, optical, UV, and gamma-ray light curves, with a time lag of less than one day. The amplitude of the IR variability is comparable to that in gamma-rays, and larger than at optical or UV wavelengths. The X-ray flux is not correlated with either the gamma-rays or longer wavelength data. These variability characteristics find a natural explanation in the external Compton model, in which electrons with Lorentz factor ? ~ 103-4 radiate synchrotron emission in the IR-optical and also scatter accretion disk or emission line photons to gamma-ray energies, while much cooler electrons (? ~ 101-2) produce X-rays by scattering synchrotron or other ambient photons.

Correlated variability in the blazar 3c 454.3

Some quantum measurements cannot be performed simultaneously; i.e., they are incompatible. Here we show that every set of incompatible measurements provides an advantage over compatible ones in a suitably chosen quantum state discrimination task. This is proven by showing that the robustness of incompatibility, a quantifier of how much noise a set of measurements tolerates before becoming compatible, has an operational interpretation as the advantage in an optimally chosen discrimination task. We also show that if we take a resource-theory perspective of measurement incompatibility, then the guessing probability in discrimination tasks of this type forms a complete set of monotones that completely characterize the partial order in the resource theory. Finally, we make use of previously known relations between measurement incompatibility and Einstein-Podolsky-Rosen steering to also relate the latter with quantum state discrimination.

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All Sets of Incompatible Measurements give an Advantage in Quantum State Discrimination

We consider a special form of state discrimination in which after the measurement we are given additional information that may help us identify the state. This task plays a central role in the analysis of quantum cryptographic protocols in the noisy-storage model, where the identity of the state corresponds to a certain bit string, and the additional information is typically a choice of encoding that is initially unknown to the cheating party. We first provide simple optimality conditions for measurements for any such problem and show upper and lower bounds on the success probability. For a certain class of problems, we furthermore provide tight bounds on how useful postmeasurement information can be. In particular, we show that for this class finding the optimal measurement for the task of state discrimination with postmeasurement information does in fact reduce to solving a different problem of state discrimination without such information. However, we show that for the corresponding classical state discrimination problems with postmeasurement information such a reduction is impossible, by relating the success probability to the violation of Bell inequalities. This suggests the usefulness of postmeasurement information as another feature that distinguishes the classical from a quantum world.

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Using postmeasurement information in state discrimination

Quantifying the speed of linguistic change is challenging because the historical evolution of languages is sparsely documented. Consequently, traditional methods rely on phylogenetic reconstruction. Here, we propose a model-based approach to the problem through the analysis of language change as a stochastic process combining vertical descent, spatial interactions, and mutations in both dimensions. A notion of linguistic temperature emerges naturally from this analysis as a dimensionless measure of the propensity of a linguistic feature to undergo change. We demonstrate how temperatures of linguistic features can be inferred from their present-day geospatial distributions, without recourse to information about their phylogenies. Thus, the evolutionary dynamics of language, operating across thousands of years, leave a measurable geospatial signature. This signature licenses inferences about the historical evolution of languages even in the absence of longitudinal data.

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Geospatial distributions reflect temperatures of linguistic features

Multilingual Manchester: A Digest

Different structural features of human language change at different rates and thus exhibit different temporal stabilities. Existing methods of linguistic stability estimation depend upon the prior genealogical classification of the world's languages into language families; these methods result in unreliable stability estimates for features which are sensitive to horizontal transfer between families and whenever data are aggregated from families of divergent time depths. To overcome these problems, we describe a method of stability estimation without family classifications, based on mathematical modelling and the analysis of contemporary geospatial distributions of linguistic features. Regressing the estimates produced by our model against those of a genealogical method, we report broad agreement but also important differences. In particular, we show that our approach is not liable to some of the false positives and false negatives incurred by the genealogical method. Our results suggest that the historical evolution of a linguistic feature leaves a footprint in its global geospatial distribution, and that rates of evolution can be recovered from these distributions by treating language dynamics as a spatially extended stochastic process.

Geospatial distributions reflect rates of evolution of features of language

Languages other than English are part of the cultural heritage of a significant and growing proportion of the British population. • In 2011, 8% of the population reported a main language other than English (or Welsh in Wales) and it is likely that this is a small fraction of all people in England and Wales who consider another language a part of their lives. • The languages found in England and Wales are diverse: – from languages local to this region such as Welsh and Irish, to other European languages such as French, Portuguese, and Polish; – Middle Eastern and West Asian languages such as Arabic, Turkish, Persian, and Kurdish; – South Asian languages such as Urdu, Panjabi, and Bengali; – East and South-East Asian languages such as Chinese, Vietnamese, and Thai; – East African languages such as Somali, Amharic, and Tigrinya; – Nigerian and other West African languages such as Yoruba and Igbo.

Deepthi Gopal

Papers

Using postmeasurement information in state discrimination

Geospatial distributions reflect temperatures of linguistic features

Multilingual Manchester: A Digest

Geospatial distributions reflect rates of evolution of features of language

What languages are spoken in England and Wales