Proposed experiment to test the bounds of quantum correlations

Clauser-Horne-Shimony-Holt inequality can give values between the classical bound, 2, and Tsirelson's bound, 2 \sqrt 2. However, for a given set of local observables, there are values in this range which no quantum state can attain. We provide the analytical expression for the corresponding bound for a parametrization of the local observables introduced by Filipp and Svozil, and describe how to experimentally trace it using a source of singlet states. Such an experiment will be useful to identify the origin of the experimental errors in Bell's inequality-type experiments and could be modified to detect hypothetical correlations beyond those predicted by quantum mechanics.Comment: REVTeX4, 4 pages, 2 figure

Interconversion of Nonlocal Correlations

In this paper we study the correlations that arise when two separated parties perform measurements on systems they hold locally. We restrict ourselves to those correlations with which arbitrarily fast transmission of information is impossible. These correlations are called nonsignaling. We allow the measurements to be chosen from sets of an arbitrary size, but promise that each measurement has only two possible outcomes. We find the structure of this convex set of nonsignaling correlations by characterizing its extreme points. Taking an information-theoretic view, we prove that all of these extreme correlations are interconvertible. This suggests that the simplest extremal nonlocal distribution (called a PR box) might be the basic unit of nonlocality. We also show that this unit of nonlocality is sufficient to simulate all quantum states when measured with two outcome measurements.Comment: 7 pages + appendix, single colum

Causality and Cirel'son bounds

An EPR-Bell type experiment carried out on an entangled quantum system can produce correlations stronger than allowed by local realistic theories. However there are correlations that are no-signaling and are more non local than the quantum correlations. Here we show that any correlations more non local than those achievable in an EPR-Bell type experiment necessarily allow -in the context of the quantum formalism- both for signaling and for generation of entanglement. We use our approach to rederive Cirel'son bound for the CHSH expression, and we derive a new Cirel'son type bound for qutrits. We discuss in detail the interpretation of our approach.Comment: 5 page

Distilling Non-Locality

Two parts of an entangled quantum state can have a correlation in their joint behavior under measurements that is unexplainable by shared classical information. Such correlations are called non-local and have proven to be an interesting resource for information processing. Since non-local correlations are more useful if they are stronger, it is natural to ask whether weak non-locality can be amplified. We give an affirmative answer by presenting the first protocol for distilling non-locality in the framework of generalized non-signaling theories. Our protocol works for both quantum and non-quantum correlations. This shows that in many contexts, the extent to which a single instance of a correlation can violate a CHSH inequality is not a good measure for the usefulness of non-locality. A more meaningful measure follows from our results.Comment: Revised abstract, introduction and conclusion. Accepted by PR

How much larger quantum correlations are than classical ones

Considering as distance between two two-party correlations the minimum number of half local results one party must toggle in order to turn one correlation into the other, we show that the volume of the set of physically obtainable correlations in the Einstein-Podolsky-Rosen-Bell scenario is (3 pi/8)^2 = 1.388 larger than the volume of the set of correlations obtainable in local deterministic or probabilistic hidden-variable theories, but is only 3 pi^2/32 = 0.925 of the volume allowed by arbitrary causal (i.e., no-signaling) theories.Comment: REVTeX4, 6 page

Can one see entanglement ?

The human eye can detect optical signals containing only a few photons. We investigate the possibility to demonstrate entanglement with such biological detectors. While one person could not detect entanglement by simply observing photons, we discuss the possibility for several observers to demonstrate entanglement in a Bell-type experiment, in which standard detectors are replaced by human eyes. Using a toy model for biological detectors that captures their main characteristic, namely a detection threshold, we show that Bell inequalities can be violated, thus demonstrating entanglement. Remarkably, when the response function of the detector is close to a step function, quantum non-locality can be demonstrated without any further assumptions. For smoother response functions, as for the human eye, post-selection is required.Comment: 5 pages, 5 figure

Tsirelson's problem and Kirchberg's conjecture

Tsirelson's problem asks whether the set of nonlocal quantum correlations with a tensor product structure for the Hilbert space coincides with the one where only commutativity between observables located at different sites is assumed. Here it is shown that Kirchberg's QWEP conjecture on tensor products of C*-algebras would imply a positive answer to this question for all bipartite scenarios. This remains true also if one considers not only spatial correlations, but also spatiotemporal correlations, where each party is allowed to apply their measurements in temporal succession; we provide an example of a state together with observables such that ordinary spatial correlations are local, while the spatiotemporal correlations reveal nonlocality. Moreover, we find an extended version of Tsirelson's problem which, for each nontrivial Bell scenario, is equivalent to the QWEP conjecture. This extended version can be conveniently formulated in terms of steering the system of a third party. Finally, a comprehensive mathematical appendix offers background material on complete positivity, tensor products of C*-algebras, group C*-algebras, and some simple reformulations of the QWEP conjecture.Comment: 57 pages, to appear in Rev. Math. Phy

Tsirelson bounds for generalized Clauser-Horne-Shimony-Holt inequalities

Quantum theory imposes a strict limit on the strength of non-local correlations. It only allows for a violation of the CHSH inequality up to the value 2 sqrt(2), known as Tsirelson's bound. In this note, we consider generalized CHSH inequalities based on many measurement settings with two possible measurement outcomes each. We demonstrate how to prove Tsirelson bounds for any such generalized CHSH inequality using semidefinite programming. As an example, we show that for any shared entangled state and observables X_1,...,X_n and Y_1,...,Y_n with eigenvalues +/- 1 we have | + <X_2 Y_1> + + + ... + - | <= 2 n cos(pi/(2n)). It is well known that there exist observables such that equality can be achieved. However, we show that these are indeed optimal. Our approach can easily be generalized to other inequalities for such observables.Comment: 9 pages, LateX, V2: Updated reference [3]. To appear in Physical Review