86,215 research outputs found
Random Numbers Certified by Bell's Theorem
Randomness is a fundamental feature in nature and a valuable resource for
applications ranging from cryptography and gambling to numerical simulation of
physical and biological systems. Random numbers, however, are difficult to
characterize mathematically, and their generation must rely on an unpredictable
physical process. Inaccuracies in the theoretical modelling of such processes
or failures of the devices, possibly due to adversarial attacks, limit the
reliability of random number generators in ways that are difficult to control
and detect. Here, inspired by earlier work on nonlocality based and device
independent quantum information processing, we show that the nonlocal
correlations of entangled quantum particles can be used to certify the presence
of genuine randomness. It is thereby possible to design of a new type of
cryptographically secure random number generator which does not require any
assumption on the internal working of the devices. This strong form of
randomness generation is impossible classically and possible in quantum systems
only if certified by a Bell inequality violation. We carry out a
proof-of-concept demonstration of this proposal in a system of two entangled
atoms separated by approximately 1 meter. The observed Bell inequality
violation, featuring near-perfect detection efficiency, guarantees that 42 new
random numbers are generated with 99% confidence. Our results lay the
groundwork for future device-independent quantum information experiments and
for addressing fundamental issues raised by the intrinsic randomness of quantum
theory.Comment: 10 pages, 3 figures, 16 page appendix. Version as close as possible
to the published version following the terms of the journa
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
Semi-device-independent framework based on natural physical assumptions
The semi-device-independent approach provides a framework for
prepare-and-measure quantum protocols using devices whose behavior must not be
characterized nor trusted, except for a single assumption on the dimension of
the Hilbert space characterizing the quantum carriers. Here, we propose instead
to constrain the quantum carriers through a bound on the mean value of a
well-chosen observable. This modified assumption is physically better motivated
than a dimension bound and closer to the description of actual experiments. In
particular, we consider quantum optical schemes where the source emits quantum
states described in an infinite-dimensional Fock space and model our assumption
as an upper bound on the average photon number in the emitted states. We
characterize the set of correlations that may be exhibited in the simplest
possible scenario compatible with our new framework, based on two
energy-constrained state preparations and a two-outcome measurement.
Interestingly, we uncover the existence of quantum correlations exceeding the
set of classical correlations that can be produced by devices behaving in a
purely pre-determined fashion (possibly including shared randomness). This
feature suggests immediate applications to certified randomness generation.
Along this line, we analyze the achievable correlations in several
prepare-and-measure optical schemes with a mean photon number constraint and
demonstrate that they allow for the generation of certified randomness. Our
simplest optical scheme works by the on-off keying of an attenuated laser
source followed by photocounting. It opens the path to more sophisticated
energy-constrained semi-device-independent quantum cryptography protocols, such
as quantum key distribution.Comment: 26 pages, 10 figure
Optimal randomness generation from optical Bell experiments
Genuine randomness can be certified from Bell tests without any detailed
assumptions on the working of the devices with which the test is implemented.
An important class of experiments for implementing such tests is optical setups
based on polarisation measurements of entangled photons distributed from a
spontaneous parametric down conversion source. Here we compute the maximal
amount of randomness which can be certified in such setups under realistic
conditions. We provide relevant yet unexpected numerical values for the
physical parameters and achieve four times more randomness than previous
methods.Comment: 15 pages, 4 figure
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
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