964 research outputs found
On constructions of quantum-secure device-independent randomness expansion protocols
Device-independent randomness expansion protocols aim to expand a short uniformly random string into a much longer one whilst guaranteeing that their output is truly random. They are device-independent in the sense that this guarantee does not dependent on the specifics of an implementation. Rather, through the observation of nonlocal correlations we can conclude that the outputs generated are necessarily random. This thesis reports a general method for constructing these protocols and evaluating their security. Using this method, we then construct several explicit protocols and analyse their performance on noisy qubit systems. With a view towards near-future quantum technologies, we also investigate whether randomness expansion is possible using current nonlocality experiments. We find that, by combining the recent theoretical and experimental advances, it is indeed now possible to reliably and securely expand randomness
Maximal randomness expansion from steering inequality violations using qudits
We consider the generation of randomness based upon the observed violation of
an Einstein-Podolsky-Rosen (EPR) steering inequality, known as one-sided
device-independent randomness expansion. We show that in the simplest scenario
-- involving only two parties applying two measurements with outcomes each
-- that there exist EPR steering inequalities whose maximal violation certifies
the maximal amount of randomness, equal to log(d) bits. We further show that
all pure partially entangled full-Schmidt-rank states in all dimensions can
achieve maximal violation of these inequalities, and thus lead to maximal
randomness expansion in the one-sided device-independent setting. More
generally, the amount of randomness that can be certified is given by a
semidefinite program, which we use to study the behaviour for non-maximal
violations of the inequalities.Comment: 6 pages, 1 figur
High speed self-testing quantum random number generation without detection loophole
Quantum mechanics provides means of generating genuine randomness that is
impossible with deterministic classical processes. Remarkably, the
unpredictability of randomness can be certified in a self-testing manner that
is independent of implementation devices. Here, we present an experimental
demonstration of self-testing quantum random number generation based on an
detection-loophole free Bell test with entangled photons. In the randomness
analysis, without the assumption of independent identical distribution, we
consider the worst case scenario that the adversary launches the most powerful
attacks against quantum adversary. After considering statistical fluctuations
and applying an 80 Gb 45.6 Mb Toeplitz matrix hashing, we achieve a
final random bit rate of 114 bits/s, with a failure probability less than
. Such self-testing random number generators mark a critical step
towards realistic applications in cryptography and fundamental physics tests.Comment: 34 pages, 10 figure
Quantum magic rectangles: Characterization and application to certified randomness expansion
We study a generalization of the Mermin-Peres magic square game to arbitrary
rectangular dimensions. After exhibiting some general properties, these
rectangular games are fully characterized in terms of their optimal win
probabilities for quantum strategies. We find that for rectangular
games of dimensions there are quantum strategies that win with
certainty, while for dimensions quantum strategies do not
outperform classical strategies. The final case of dimensions is
richer, and we give upper and lower bounds that both outperform the classical
strategies. Finally, we apply our findings to quantum certified randomness
expansion to find the noise tolerance and rates for all magic rectangle games.
To do this, we use our previous results to obtain the winning probability of
games with a distinguished input for which the devices give a deterministic
outcome, and follow the analysis of C. A. Miller and Y. Shi [SIAM J. Comput.
46, 1304 (2017)].Comment: 23 pages, 3 figures; published version with minor correction
Device-independent randomness expansion against quantum side information
The ability to produce random numbers that are unknown to any outside party
is crucial for many applications. Device-independent randomness generation does
not require trusted devices and therefore provides strong guarantees of the
security of the output, but it comes at the price of requiring the violation of
a Bell inequality for implementation. A further challenge is to make the bounds
in the security proofs tight enough to allow randomness expansion with
contemporary technology. Although randomness has been generated in recent
experiments, the amount of randomness consumed in doing so has been too high to
certify expansion based on existing theory. Here we present an experiment that
demonstrates device-independent randomness expansion. By developing a Bell test
setup with a single-photon detection efficiency of around and by using a
spot-checking protocol, we achieve a net gain of certified
bits with a soundness error . The experiment ran for
h, which corresponds to an average rate of randomness generation of
bits per second. By developing the entropy accumulation theorem, we establish
security against quantum adversaries. We anticipate that this work will lead to
further improvements that push device-independence towards commercial
viability.Comment: v2: Update to match published version. Small error in the
term in Theorem 3 in the published supplementary information corrected her
Improvements on Device Independent and Semi-Device Independent Protocols of Randomness Expansion
To generate genuine random numbers, random number generators based on quantum theory are essential. However, ensuring that the process used to produce randomness meets desired security standards can pose challenges for traditional quantum random number generators. This thesis delves into Device Independent (DI) and Semi-Device Independent (semi-DI) protocols of randomness expansion, based on a minimal set of experimentally verifiable security assumptions. The security in DI protocols relies on the violation of Bell inequalities, which certify the quantum behavior of devices. The semi-DI protocols discussed in this thesis require the characterization of only one device - a power meter. These protocols exploit the fact that quantum states can be prepared such that they cannot be distinguished with certainty, thereby creating a randomness resource. In this study, we introduce enhanced DI and semi-DI protocols that surpass existing ones in terms of output randomness rate, security, or in some instances, both. Our analysis employs the Entropy Accumulation Theorem (EAT) to determine the extractable randomness for finite rounds. A notable contribution is the introduction of randomness expansion protocols that recycle input randomness, significantly enhancing finite round randomness rates for DI protocols based on the CHSH inequality violation. In the final section of the thesis, we delve into Generalized Probability Theories (GPTs), with a focus on Boxworld, the largest GPT capable of producing correlations consistent with relativity. A tractable criterion for identifying a Boxworld channel is presented
- …