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

Device-independent Certification of One-shot Distillable Entanglement

Entanglement sources that produce many entangled states act as a main component in applications exploiting quantum physics such as quantum communication and cryptography. Realistic sources are inherently noisy, cannot run for an infinitely long time, and do not necessarily behave in an independent and identically distributed manner. An important question then arises -- how can one test, or certify, that a realistic source produces high amounts of entanglement? Crucially, a meaningful and operational solution should allow us to certify the entanglement which is available for further applications after performing the test itself (in contrast to assuming the availability of an additional source which can produce more entangled states, identical to those which were tested). To answer the above question and lower bound the amount of entanglement produced by an uncharacterised source, we present a protocol that can be run by interacting classically with uncharacterised (but not entangled to one another) measurement devices used to measure the states produced by the source. A successful run of the protocol implies that the remaining quantum state has high amounts of one-shot distillable entanglement. That is, one can distill many maximally entangled states out of the single remaining state. Importantly, our protocol can tolerate noise and, thus, certify entanglement produced by realistic sources. With the above properties, the protocol acts as the first "operational device-independent entanglement certification protocol" and allows one to test and benchmark uncharacterised entanglement sources which may be otherwise incomparable

Simulation of equatorial von Neumann measurements on GHZ states using nonlocal resources

Reproducing with elementary resources the correlations that arise when a quantum system is measured (quantum state simulation), allows one to get insight on the operational and computational power of quantum correlations. We propose a family of models that can simulate von Neumann measurements in the x-y plane of the Bloch sphere on n-partite GHZ states using only bipartite nonlocal boxes. For the tripartite and fourpartite states, the models use only bipartite nonlocal boxes; they can be translated into classical communication schemes with finite average communication cost.Comment: 15 pages, 4 figures, 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

Noise-resistant device-independent certification of Bell state measurements

Device-independent certification refers to the characterization of an apparatus without reference to the internal description of other devices. It is a trustworthy certification method, free of assumption on the underlying Hilbert space dimension and on calibration methods. We show how it can be used to quantify the quality of a Bell state measurement, whether deterministic, partial or probabilistic. Our certification is noise resistant and opens the way towards the device-independent self-testing of Bell state measurements in existing experiments.Comment: 5+5 pages, 3+3 figures. See also related work by Marc Olivier Renou et a

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

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

Simple Buehler-optimal confidence intervals on the average success probability of independent Bernoulli trials

One-sided confidence intervals are presented for the average of non-identical Bernoulli parameters. These confidence intervals are expressed as analytical functions of the total number of Bernoulli games won, the number of rounds and the confidence level. Tightness of these bounds in the sense of Buehler, i.e. as the strictest possible monotonic intervals, is demonstrated for all confidence levels. A simple interval valid for all confidence levels is also provided with a tightness guarantee. Finally, an application of the proposed confidence intervals to sequential sampling is discussed.Comment: 15 pages, 1 figure, 2 table

Bipartite nonlocality with a many-body system

We consider a bipartite scenario where two parties hold ensembles of $1/2$-spins which can only be measured collectively. We give numerical arguments supporting the conjecture that in this scenario no Bell inequality can be violated for arbitrary numbers of spins if only first order moment observables are available. We then give a recipe to achieve a significant Bell violation with a split many-body system when this restriction is lifted. This highlights the strong requirements needed to detect bipartite quantum correlations in many-body systems device-independently.Comment: 7+5 pages, 4 figure