9 research outputs found
Certified randomness in quantum physics
The concept of randomness plays an important role in many disciplines. On one
hand, the question of whether random processes exist is fundamental for our
understanding of nature. On the other hand, randomness is a resource for
cryptography, algorithms and simulations. Standard methods for generating
randomness rely on assumptions on the devices that are difficult to meet in
practice. However, quantum technologies allow for new methods for generating
certified randomness. These methods are known as device-independent because do
not rely on any modeling of the devices. Here we review the efforts and
challenges to design device-independent randomness generators.Comment: 18 pages, 3 figure
Randomness amplification against no-signaling adversaries using two devices
Recently, a physically realistic protocol amplifying the randomness of
Santha-Vazirani sources producing cryptographically secure random bits was
proposed; however for reasons of practical relevance, the crucial question
remained open whether this can be accomplished under the minimal conditions
necessary for the task. Namely, is it possible to achieve randomness
amplification using only two no-signaling components and in a situation where
the violation of a Bell inequality only guarantees that some outcomes of the
device for specific inputs exhibit randomness? Here, we solve this question and
present a device-independent protocol for randomness amplification of
Santha-Vazirani sources using a device consisting of two non-signaling
components. We show that the protocol can amplify any such source that is not
fully deterministic into a fully random source while tolerating a constant
noise rate and prove the composable security of the protocol against general
no-signaling adversaries. Our main innovation is the proof that even the
partial randomness certified by the two-party Bell test (a single input-output
pair () for which the conditional probability
is bounded away from for all no-signaling
strategies that optimally violate the Bell inequality) can be used for
amplification. We introduce the methodology of a partial tomographic procedure
on the empirical statistics obtained in the Bell test that ensures that the
outputs constitute a linear min-entropy source of randomness. As a technical
novelty that may be of independent interest, we prove that the Santha-Vazirani
source satisfies an exponential concentration property given by a recently
discovered generalized Chernoff bound.Comment: 15 pages, 3 figure
Finite Device-Independent Extraction of a Block Min-Entropy Source against Quantum Adversaries
The extraction of randomness from weakly random seeds is a problem of central
importance with multiple applications. In the device-independent setting, this
problem of quantum randomness amplification has been mainly restricted to
specific weak sources of Santha-Vazirani type, while extraction from the
general min-entropy sources has required a large number of separated devices
which is impractical. In this paper, we present a device-independent protocol
for amplification of a single min-entropy source (consisting of two blocks of
sufficiently high min-entropy) using a device consisting of two spatially
separated components and show a proof of its security against general quantum
adversaries.Comment: 17 page
Practical randomness amplification and privatisation with implementations on quantum computers
We present an end-to-end and practical randomness amplification and
privatisation protocol based on Bell tests. This allows the building of
device-independent random number generators which output (near-)perfectly
unbiased and private numbers, even if using an uncharacterised quantum device
potentially built by an adversary. Our generation rates are linear in the
repetition rate of the quantum device and the classical randomness
post-processing has quasi-linear complexity - making it efficient on a standard
personal laptop. The statistical analysis is also tailored for real-world
quantum devices.
Our protocol is then showcased on several different quantum computers.
Although not purposely built for the task, we show that quantum computers can
run faithful Bell tests by adding minimal assumptions. In this
semi-device-independent manner, our protocol generates (near-)perfectly
unbiased and private random numbers on today's quantum computers.Comment: Important revisions and improvements to v1. inc. new sections,
improvements to protocol itself and addition of full technical appendixes.
29+23 pages (15 figures and 2 tables