Related papers: Arising information regularities in an observer
Our understanding of complex systems rests on our ability to characterise how they perform distributed computation and integrate information. Advances in information theory have introduced several quantities to describe complex information…
I formulate an entropy-rate maximization problem at the observable level for stochastic processes observed through an information-reducing observation map. For a visible stationary law, the map determines an observational fiber of hidden…
We present an iterative algorithm that finds the optimal measurement for extracting the accessible information in any quantum communication scenario. The maximization is achieved by a steepest-ascent approach toward the extremal point,…
Quantum computing and the workings of the brain have many aspects in common and have been attracting increasing attention in academia and industry. The computation in both is parallel and non-discrete. Though the underlying physical…
Interactions between pieces of information (entities) play a substantial role in the way an individual acts on them: adoption of a product, the spread of news, strategy choice, etc. However, the underlying interaction mechanisms are often…
The projected ensemble -- an ensemble of pure states on a subsystem conditioned on projective measurement outcomes on its complement -- provides a finer probe of ergodicity and information structure than the reduced density matrix of the…
The number of observable degrees of freedom is typically limited in experiments. Here, we consider discrete Markov networks in which an observer has access to a few visible transitions and the waiting times between these transitions.…
A unified combinatorial definition of the information content and entropy of different types of patterns, compatible with the traditional concepts of information and entropy, going beyond the limitations of Shannon information interpretable…
In spite of many results in quantum information theory, the complex nature of compound systems is far from being clear. In general the information is a mixture of local, and non-local ("quantum") information. To make this point more clear,…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible while constrained to match empirically estimated feature expectations. However, in many real-world…
Measurements transfer information about a system to the apparatus, and then further on -- to observers and (often inadvertently) to the environment. I show that even imperfect copying essential in such situations restricts possible…
Our capacity to process information depends on the computational power at our disposal. Information theory captures our ability to distinguish states or communicate messages when it is unconstrained with unrivaled beauty and elegance. For…
We characterize information as risk reduction between knowledge states represented by partitions of the underlying probability space. Entropy corresponds to risk reduction from no (or partial) knowledge to full knowledge about a random…
Algorithmic information theory roots the concept of information in computation rather than probability. These lecture notes were constructed in conjunction with the graduate course I taught at Universit\`a della Svizzera italiana in the…
The class of problems in causal inference which seeks to isolate causal correlations solely from observational data even without interventions has come to the forefront of machine learning, neuroscience and social sciences. As new large…
The quantum prepare-and-measure scenario has been studied under various physical assumptions on the emitted states. Here, we first discuss how different assumptions are conceptually and formally related. We then identify one that can serve…
We try to establish a unified information theoretic approach to learning and to explore some of its applications. First, we define {\em predictive information} as the mutual information between the past and the future of a time series,…
Extracting higher-order structures from multivariate data has become an area of intensive study in complex systems science, as these multipartite interactions can reveal insights into fundamental features of complex systems like emergent…
Quantum computation has been growing rapidly in both theory and experiments. In particular, quantum computing devices with a large number of qubits have been developed by IBM, Google, IonQ, and others. The current quantum computing devices…
A new measure of information in quantum mechanics is proposed which takes into account that for quantum systems the only feature known before an experiment is performed are the probabilities for various events to occur. The sum of the…