1,341 research outputs found
Duality Between Smooth Min- and Max-Entropies
In classical and quantum information theory, operational quantities such as
the amount of randomness that can be extracted from a given source or the
amount of space needed to store given data are normally characterized by one of
two entropy measures, called smooth min-entropy and smooth max-entropy,
respectively. While both entropies are equal to the von Neumann entropy in
certain special cases (e.g., asymptotically, for many independent repetitions
of the given data), their values can differ arbitrarily in the general case.
In this work, a recently discovered duality relation between (non-smooth)
min- and max-entropies is extended to the smooth case. More precisely, it is
shown that the smooth min-entropy of a system A conditioned on a system B
equals the negative of the smooth max-entropy of A conditioned on a purifying
system C. This result immediately implies that certain operational quantities
(such as the amount of compression and the amount of randomness that can be
extracted from given data) are related. Such relations may, for example, have
applications in cryptographic security proofs
A Fully Quantum Asymptotic Equipartition Property
The classical asymptotic equipartition property is the statement that, in the
limit of a large number of identical repetitions of a random experiment, the
output sequence is virtually certain to come from the typical set, each member
of which is almost equally likely. In this paper, we prove a fully quantum
generalization of this property, where both the output of the experiment and
side information are quantum. We give an explicit bound on the convergence,
which is independent of the dimensionality of the side information. This
naturally leads to a family of Renyi-like quantum conditional entropies, for
which the von Neumann entropy emerges as a special case.Comment: Main claim is updated with improved bound
Robust Randomness Amplifiers: Upper and Lower Bounds
A recent sequence of works, initially motivated by the study of the nonlocal
properties of entanglement, demonstrate that a source of
information-theoretically certified randomness can be constructed based only on
two simple assumptions: the prior existence of a short random seed and the
ability to ensure that two black-box devices do not communicate (i.e. are
non-signaling). We call protocols achieving such certified amplification of a
short random seed randomness amplifiers.
We introduce a simple framework in which we initiate the systematic study of
the possibilities and limitations of randomness amplifiers. Our main results
include a new, improved analysis of a robust randomness amplifier with
exponential expansion, as well as the first upper bounds on the maximum
expansion achievable by a broad class of randomness amplifiers. In particular,
we show that non-adaptive randomness amplifiers that are robust to noise cannot
achieve more than doubly exponential expansion. Finally, we show that a wide
class of protocols based on the use of the CHSH game can only lead to (singly)
exponential expansion if adversarial devices are allowed the full power of
non-signaling strategies. Our upper bound results apply to all known
non-adaptive randomness amplifier constructions to date.Comment: 28 pages. Comments welcom
Navigating the Social Landscape: An Exploration of Social Networking Site Usage among Emerging Adults
This study explores how emerging adults (Arnett, 2000) in their first- and second-year of undergraduate study make use of social networking sites (SNSs) for their day-to-day sociality. This study compares emerging adults’ use of Facebook, which is the most popular and widely used SNS among this particular demographic, to increasingly popular SNSs Twitter and Instagram. This project seeks to discover how the use of different SNSs supplements, changes, or replaces the use of Facebook, considering social capital exists on each platform, and if and how each sites’ uses and gratifications differ. This study employs face-to-face semi-structured interviews to pursue the proposed research questions, using a grounded theory approach informed by social capital and uses and gratifications theory
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