Related papers: Integrated Information in Process Theories
Broadly speaking Information theory (IT) assumes no structure of the underlying states. But what about contexts where states do have a clear structure - how should IT cope with such situations? And if such coping is at all possible then -…
Qudits have proven to be a powerful resource for quantum information processing, offering enhanced channel capacities, improved robustness to noise, and highly efficient implementations of quantum algorithms. The encoding of photonic qudits…
The field of Information Theory is founded on Claude Shannon's seminal ideas relating to entropy. Nevertheless, his well-known avoidance of meaning (Shannon, 1948) still persists to this day, so that Information Theory remains poorly…
Quantum information and computation may serve as a source of useful axioms and ideas for the quantum logic/quantum structures project of characterizing and classifying types of physical theories, including quantum mechanics and classical…
A remarkable feature of quantum theory is that particles with identical intrinsic properties must be treated as indistinguishable if the theory is to give valid predictions. In the quantum formalism, indistinguishability is expressed via…
The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This review aims to summarise not just quantum computing, but the whole subject of quantum information theory.…
Informational dependence between statistical or quantum subsystems can be described with Fisher matrix or Fubini-Study metric obtained from variations of the sample/configuration space coordinates. Using these non-covariant objects as…
After more than a century since its birth, Quantum Theory still eludes our understanding. If asked to describe it, we have to resort to abstract and ad hoc principles about complex Hilbert spaces. How is it possible that a fundamental…
The ability to integrate information in the brain is considered to be an essential property for cognition and consciousness. Integrated Information Theory (IIT) hypothesizes that the amount of integrated information ($\Phi$) in the brain is…
We show that Coecke's compositionality theorem for quantum information flow follows by the universal property of tensor products from the case in which all relevant states are totally disentangled, for which the proof is almost trivial.…
We propose a new interpretation of measures of information and disorder by connecting these concepts to group theory in a new way. Entropy and group theory are connected here by their common relation to sets of permutations. A combinatorial…
A practical notation can convey valuable intuitions and concisely express new ideas. Information theory is of importance to machine learning, but the notation for information-theoretic quantities is sometimes opaque. We propose a practical…
Since 2004, researchers have been using the mathematical framework of Quantum Theory (QT) in Information Retrieval (IR). QT offers a generalized probability and logic framework. Such a framework has been shown capable of unifying the…
This paper addresses theoretically correct vs. incorrect ways to apply information theory to point processes.
Quantum mechanics is a cornerstone of our current understanding of nature and extremely successful in describing physics covering a huge range of scales. However, its interpretation remains controversial since the early days of quantum…
We develop a notion of iterated monoidal category and show that this notion corresponds in a precise way to the notion of iterated loop space. Specifically the group completion of the nerve of such a category is an iterated loop space and…
We present a discussion of generalized statistics based on Renyi's, Fisher's and Tsallis's measures of information. The unifying conceptual framework which we employ here is provided by information theory. Important applications of…
Complex systems often exhibit multiple levels of organization covering a wide range of physical scales, so the study of the hierarchical decomposition of their structure and function is frequently convenient. To better understand this…
Monoidal computer is a categorical model of intensional computation, where many different programs correspond to the same input-output behavior. The upshot of yet another model of computation is that a categorical formalism should provide a…
The experience from Quantum Information has lead us to look at Quantum Theory (QT) and the whole Physics from a different angle. The information-theoretical paradigm---"It from Bit'---prophesied by John Archibald Wheeler is relentlessly…