More randomness from noisy sources

Bell experiments can be used to generate private random numbers. An ideal Bell experiment would involve measuring a state of two maximally entangled qubits, but in practice any state produced is subject to noise. Here we consider how the techniques presented in arXiv:1309.3894 and arXiv:1309.3930, i.e. using an optimized Bell inequality, and taking advantage of the fact that the device provider is not our adversary, can be used to improve the rate of randomness generation in Bell-like tests performed on singlet states subject to either white or dephasing noise.Comment: 4 pages, 2 figures; to appear in Proceedings of TQC 2014; published versio

More Randomness from the Same Data

Correlations that cannot be reproduced with local variables certify the generation of private randomness. Usually, the violation of a Bell inequality is used to quantify the amount of randomness produced. Here, we show how private randomness generated during a Bell test can be directly quantified from the observed correlations, without the need to process these data into an inequality. The frequency with which the different measurement settings are used during the Bell test can also be taken into account. This improved analysis turns out to be very relevant for Bell tests performed with a finite collection efficiency. In particular, applying our technique to the data of a recent experiment [Christensen et al., Phys. Rev. Lett. 111, 130406 (2013)], we show that about twice as much randomness as previously reported can be potentially extracted from this setup.Comment: 6 pages + appendices, 4 figures, v3: version close to the published one. See also the related work arXiv:1309.393

Analysis of a proposal for a realistic loophole-free Bell test with atom-light entanglement

The violation of Bell inequalities where both detection and locality loopholes are closed is crucial for device independent assessments of quantum information. While of technological nature, the simultaneous closing of both loopholes still remains a challenge. In Nat. Commun. 4:2104(2013), a realistic setup to produce an atom-photon entangled state that could reach a loophole free Bell inequality violation within current experimental technology was proposed. Here we improve the analysis of this proposal by giving an analytical treatment that shows that the state proposed in Nat. Commun. 4:2104(2013) could in principle violate a Bell inequality for arbitrarily low photodetection efficiency. Moreover, it is also able to violate a Bell inequality considering only atomic and homodyne measurements eliminating the need to consider inefficient photocounting measurements. In this case, the maximum Clauser-Horne-Shimony-Holt (CHSH) inequality violation achievable is 2.29, and the minimum transmission required for violation is about 68%. Finally, we show that by postselecting on an atomic measurement, one can engineer superpositions of coherent states for various coherent state amplitudes.Comment: 7 pages, 6 figures, to appear in Phys. Rev.

Measurement-device-independent quantification of entanglement for given Hilbert space dimension

We address the question of how much entanglement can be certified from the observed correlations and the knowledge of the Hilbert space dimension of the measured systems. We focus on the case in which both systems are known to be qubits. For several correlations (though not for all), one can certify the same amount of entanglement as with state tomography, but with fewer assumptions, since nothing is assumed about the measurements. We also present security proofs of quantum key distribution without any assumption on the measurements. We discuss how both the amount of entanglement and the security of quantum key distribution (QKD) are affected by the inefficiency of detectors in this scenario.Comment: 19 pages, 6 figure

Device-independent parallel self-testing of two singlets

Device-independent self-testing is the possibility of certifying the quantum state and the measurements, up to local isometries, using only the statistics observed by querying uncharacterized local devices. In this paper, we study parallel self-testing of two maximally entangled pairs of qubits: in particular, the local tensor product structure is not assumed but derived. We prove two criteria that achieve the desired result: a double use of the Clauser-Horne-Shimony-Holt inequality and the $3\times 3$ Magic Square game. This demonstrate that the magic square game can only be perfectly won by measureing a two-singlets state. The tolerance to noise is well within reach of state-of-the-art experiments.Comment: 9 pages, 2 figure

Bell nonlocality

Bell's 1964 theorem, which states that the predictions of quantum theory cannot be accounted for by any local theory, represents one of the most profound developments in the foundations of physics. In the last two decades, Bell's theorem has been a central theme of research from a variety of perspectives, mainly motivated by quantum information science, where the nonlocality of quantum theory underpins many of the advantages afforded by a quantum processing of information. The focus of this review is to a large extent oriented by these later developments. We review the main concepts and tools which have been developed to describe and study the nonlocality of quantum theory, and which have raised this topic to the status of a full sub-field of quantum information science.Comment: 65 pages, 7 figures. Final versio

Many-box locality

There is an ongoing search for a physical or operational definition for quantum mechanics. Several informational principles have been proposed which are satisfied by a theory less restrictive than quantum mechanics. Here, we introduce the principle of "many-box locality", which is a refined version of the previously proposed "macroscopic locality". These principles are based on coarse-graining the statistics of several copies of a given box. The set of behaviors satisfying many-box locality for $N$ boxes is denoted $MBL_N$. We study these sets in the bipartite scenario with two binary measurements, in relation with the sets $\mathcal{Q}$ and $\mathcal{Q}_{1+AB}$ of quantum and "almost quantum" correlations. We find that the $MBL_N$ sets are in general not convex. For unbiased marginals, by working in the Fourier space we can prove analytically that $MBL_{N}\subsetneq\mathcal{Q}$ for any finite $N$, while $MBL_{\infty}=\mathcal{Q}$. Then, with suitably developed numerical tools, we find an example of a point that belongs to $MBL_{16}$ but not to $\mathcal{Q}_{1+AB}$. Among the problems that remain open, is whether $\mathcal{Q}\subset MBL_{\infty}$.Comment: 10 pages, 4 figures, 2 ancillary files; v2: similar to published versio