121 research outputs found
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
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
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
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 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
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
-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
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