34 research outputs found
Generalizations of Fano's Inequality for Conditional Information Measures via Majorization Theory
Fano's inequality is one of the most elementary, ubiquitous, and important
tools in information theory. Using majorization theory, Fano's inequality is
generalized to a broad class of information measures, which contains those of
Shannon and R\'{e}nyi. When specialized to these measures, it recovers and
generalizes the classical inequalities. Key to the derivation is the
construction of an appropriate conditional distribution inducing a desired
marginal distribution on a countably infinite alphabet. The construction is
based on the infinite-dimensional version of Birkhoff's theorem proven by
R\'{e}v\'{e}sz [Acta Math. Hungar. 1962, 3, 188{\textendash}198], and the
constraint of maintaining a desired marginal distribution is similar to
coupling in probability theory. Using our Fano-type inequalities for Shannon's
and R\'{e}nyi's information measures, we also investigate the asymptotic
behavior of the sequence of Shannon's and R\'{e}nyi's equivocations when the
error probabilities vanish. This asymptotic behavior provides a novel
characterization of the asymptotic equipartition property (AEP) via Fano's
inequality.Comment: 44 pages, 3 figure
Generalized Entropies and Metric-Invariant Optimal Countermeasures for Information Leakage Under Symmetric Constraints
One again, tuition has risen at the College. However, students believe that it is higher overall than the nationwide jump which recently occurred. Both the students and staff of the College are currently dissatisfied with the library. They believe that its system of numbering should be switched over to something more modern. The funding of campus groups is looked at by the administration. William Darr, from Earlham College, will be appearing at Wooster to display his Japanese prints. Wooster recently beat Wesleyan in basketball, and hopes to go on to a championshiphttps://openworks.wooster.edu/voice1961-1970/1100/thumbnail.jp
Generalized Entropies and Metric-Invariant Optimal Countermeasures for Information Leakage Under Symmetric Constraints
We introduce a novel generalization of entropy and conditional entropy from
which most definitions from the literature can be derived as particular cases.
Within this general framework, we investigate the problem of designing
countermeasures for information leakage. In particular, we seek
metric-invariant solutions, i.e., they are robust against the choice of entropy
for quantifying the leakage. The problem can be modelled as an information
channel from the system to an adversary, and the countermeasures can be seen as
modifying this channel in order to minimise the amount of information that the
outputs reveal about the inputs. Our main result is to fully solve the problem
under the highly symmetrical design constraint that the number of inputs that
can produce the same output is capped. Our proof is constructive and the
optimal channels and the minimum leakage are derived in closed form.Comment: Accepted to IEEE Transactions on Information Theory, in November 201
Probing and detecting entanglement in synthetic quantum matter
In the past decades, rapid advances in the experimental control of quantum systems have opened up unparalleled capabilities of engineering exotic quantum states. Nowadays, we may consider ourselves witnesses of a second quantum revolution as strongly correlated quantum matter is regularly created, on a daily basis, within the most diverse platforms, e.g. arrays of Rydberg atoms, ultra-cold atoms in optical lattices, superconducting qubits, trapped ions, and quantum dots.
In this era, dubbed Noisy-Intermediate Scale Quantum (NISQ) era, the effort in pursuing research for realizing quantum technologies with practical purposes, such as quantum computing, simulations, communication and metrology, has greatly accelerated, and we are just starting to experience the immense progress that could be achieved.
The remarkable breakthrough we are facing builds upon seminal theoretical and experimental advances in quantum physics. The key achievements in atomic, molecular, and optical (AMO) physics have opened up the possibility of controlling, trapping, and measuring single atoms, one by one, with high accuracy and reliability. In parallel, from a theoretical point of view, the study of quantum entanglement and correlations has bridged AMO physics and quantum information with crucial proposals for the realization of universal quantum computers.
In this context, entanglement has emerged as one of the key tools to characterize and to exploit quantum many-body systems for quantum information purposes.
We will study quantum entanglement in several scenarios to investigate and probe complex quantum many-body systems. We will consider examples ranging from generic mixed states in equilibrium to out-of-equilibrium dynamics, with and without dissipation, and topologically non-trivial systems.
The leitmotif of this work will be how entanglement and correlations can be exploited to characterize the many-body quantum state describing a physical system and how entanglement can be detected in an experimentally efficient manner
Dynamical Systems
Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...
Complexity in Economic and Social Systems
There is no term that better describes the essential features of human society than complexity. On various levels, from the decision-making processes of individuals, through to the interactions between individuals leading to the spontaneous formation of groups and social hierarchies, up to the collective, herding processes that reshape whole societies, all these features share the property of irreducibility, i.e., they require a holistic, multi-level approach formed by researchers from different disciplines. This Special Issue aims to collect research studies that, by exploiting the latest advances in physics, economics, complex networks, and data science, make a step towards understanding these economic and social systems. The majority of submissions are devoted to financial market analysis and modeling, including the stock and cryptocurrency markets in the COVID-19 pandemic, systemic risk quantification and control, wealth condensation, the innovation-related performance of companies, and more. Looking more at societies, there are papers that deal with regional development, land speculation, and the-fake news-fighting strategies, the issues which are of central interest in contemporary society. On top of this, one of the contributions proposes a new, improved complexity measure