6,460 research outputs found
Full security of quantum key distribution from no-signaling constraints
We analyze a cryptographic protocol for generating a distributed secret key
from correlations that violate a Bell inequality by a sufficient amount, and
prove its security against eavesdroppers, constrained only by the assumption
that any information accessible to them must be compatible with the
non-signaling principle. The claim holds with respect to the state-of-the-art
security definition used in cryptography, known as universally-composable
security. The non-signaling assumption only refers to the statistics of
measurement outcomes depending on the choices of measurements; hence security
is independent of the internal workings of the devices --- they do not even
need to follow the laws of quantum theory. This is relevant for practice as a
correct and complete modeling of realistic devices is generally impossible. The
techniques developed are general and can be applied to other Bell
inequality-based protocols. In particular, we provide a scheme for estimating
Bell-inequality violations when the samples are not independent and identically
distributed.Comment: 15 pages, 2 figur
Quantum Cryptography Based Solely on Bell's Theorem
Information-theoretic key agreement is impossible to achieve from scratch and
must be based on some - ultimately physical - premise. In 2005, Barrett, Hardy,
and Kent showed that unconditional security can be obtained in principle based
on the impossibility of faster-than-light signaling; however, their protocol is
inefficient and cannot tolerate any noise. While their key-distribution scheme
uses quantum entanglement, its security only relies on the impossibility of
superluminal signaling, rather than the correctness and completeness of quantum
theory. In particular, the resulting security is device independent. Here we
introduce a new protocol which is efficient in terms of both classical and
quantum communication, and that can tolerate noise in the quantum channel. We
prove that it offers device-independent security under the sole assumption that
certain non-signaling conditions are satisfied. Our main insight is that the
XOR of a number of bits that are partially secret according to the
non-signaling conditions turns out to be highly secret. Note that similar
statements have been well-known in classical contexts. Earlier results had
indicated that amplification of such non-signaling-based privacy is impossible
to achieve if the non-signaling condition only holds between events on Alice's
and Bob's sides. Here, we show that the situation changes completely if such a
separation is given within each of the laboratories.Comment: 32 pages, v2: changed introduction, added reference
Quantifying the randomness of copies of noisy Popescu-Rohrlich correlations
In a no-signaling world, the outputs of a nonlocal box cannot be completely
predetermined, a feature that is exploited in many quantum information
protocols exploiting non-locality, such as device-independent randomness
generation and quantum key distribution. This relation between non-locality and
randomness can be formally quantified through the min-entropy, a measure of the
unpredictability of the outputs that holds conditioned on the knowledge of any
adversary that is limited only by the no-signaling principle. This quantity can
easily be computed for the noisy Popescu-Rohrlich (PR) box, the paradigmatic
example of non-locality. In this paper, we consider the min-entropy associated
to several copies of noisy PR boxes. In the case where n noisy PR-boxes are
implemented using n non-communicating pairs of devices, it is known that each
PR-box behaves as an independent biased coin: the min-entropy per PR-box is
constant with the number of copies. We show that this doesn't hold in more
general scenarios where several noisy PR-boxes are implemented from a single
pair of devices, either used sequentially n times or producing n outcome bits
in a single run. In this case, the min-entropy per PR-box is smaller than the
min-entropy of a single PR-box, and it decreases as the number of copies
increases.Comment: 14 pages + 8 figures. Mathematica files attached. Comments welcom
Limitations on device independent secure key via squashed non-locality
We initiate a systematic study to provide upper bounds on device-independent
key, secure against a non-signaling adversary (NSDI), distilled by a wide class
of operations, currently used in both quantum and non-signaling
device-independent protocols. These operations consist of a direct measurements
on the devices followed by Local Operations and Public Communication (MDLOPC).
We employ the idea of "squashing" on the secrecy monotones, which provide upper
bounds on the key rate in secret key agreement (SKA) scenario, and show that
squashed secrecy monotones are the upper bounds on NSDI key. As an important
instance, an upper bound on NSDI key rate called "squashed non-locality", has
been constructed. It exhibits several important properties, including
convexity, monotonicity, additivity on tensor products, and asymptotic
continuity. Using this bound, we identify numerically a domain of two binary
inputs and two binary outputs non-local devices for which the squashed
non-locality is zero, and therefore one can not distil key from them via MDLOPC
operations. These are mixtures of Popescu-Rohrlich (PR) and anti-PR box with
the weight of PR box less than . This example confirms the intuition that
non-locality need not imply secrecy in the non-signaling scenario. The approach
is general, describing how to construct other tighter yet possibly less
computable upper bounds. Our technique for obtaining upper bounds is based on
the non-signaling analog of quantum purification: the complete extension, which
yields equivalent security conditions as previously known in the literature.Comment: 12 pages and 2 figures + supplemental materia
Fundamental limits on key rates in device-independent quantum key distribution
In this paper, we introduce intrinsic non-locality as a quantifier for Bell
non-locality, and we prove that it satisfies certain desirable properties such
as faithfulness, convexity, and monotonicity under local operations and shared
randomness. We then prove that intrinsic non-locality is an upper bound on the
secret-key-agreement capacity of any device-independent protocol conducted
using a device characterized by a correlation . We also prove that intrinsic
steerability is an upper bound on the secret-key-agreement capacity of any
semi-device-independent protocol conducted using a device characterized by an
assemblage . We also establish the faithfulness of intrinsic
steerability and intrinsic non-locality. Finally, we prove that intrinsic
non-locality is bounded from above by intrinsic steerability.Comment: 44 pages, 4 figures, final version accepted for publication in New
Journal of Physic
Bell nonlocality
Bell's 1964 theorem, which states that the predictions of quantum theory
cannot be accounted for by any local theory, represents one of the most
profound developments in the foundations of physics. In the last two decades,
Bell's theorem has been a central theme of research from a variety of
perspectives, mainly motivated by quantum information science, where the
nonlocality of quantum theory underpins many of the advantages afforded by a
quantum processing of information. The focus of this review is to a large
extent oriented by these later developments. We review the main concepts and
tools which have been developed to describe and study the nonlocality of
quantum theory, and which have raised this topic to the status of a full
sub-field of quantum information science.Comment: 65 pages, 7 figures. Final versio
Universally-composable privacy amplification from causality constraints
We consider schemes for secret key distribution which use as a resource
correlations that violate Bell inequalities. We provide the first security
proof for such schemes, according to the strongest notion of security, the so
called universally-composable security. Our security proof does not rely on the
validity of quantum mechanics, it solely relies on the impossibility of
arbitrarily-fast signaling between separate physical systems. This allows for
secret communication in situations where the participants distrust their
quantum devices.Comment: 4 page
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
- …