Related papers: Unnormalized Measures in Information Theory
We extend algorithmic conservation inequalities to probability measures. The amount of self information of a probability measure cannot increase when submitted to randomized processing. This includes (potentially non-computable) measures…
We use a novel form of quantum conditional probability to define new measures of quantum information in a dynamical context. We explore relationships between our new quantities and standard measures of quantum information, such as von…
Generalized Probabilistic Theories (GPTs) provide a unified framework for describing probabilistic physical theories, encompassing classical and quantum theories as well as hypothetical theories beyond quantum mechanics. Since most GPTs are…
At this point in time, two major areas of physics, statistical mechanics and quantum mechanics, rest on the foundations of probability and entropy. The last century saw several significant fundamental advances in our understanding of the…
We introduce a hierarchical classification of theories that describe systems with fundamentally limited information content. This property is introduced in an operational way and gives rise to the existence of mutually complementary…
In inverse problems, one attempts to infer spatially variable functions from indirect measurements of a system. To practitioners of inverse problems, the concept of "information" is familiar when discussing key questions such as which parts…
The concept of information has emerged as a language in its own right, bridging several disciplines that analyze natural phenomena and man-made systems. Integrated information has been introduced as a metric to quantify the amount of…
We construct a probabilistic coherence measure for information sets which determines a partial coherence ordering. This measure is applied in constructing a criterion for expanding our beliefs in the face of new information. A number of…
The paper deals with measures of nonlinearity. In state estimation, they are utilized i) to select a suitable state estimation algorithm by assessing the nonlinearity of a system model, ii) to adapt the estimation algorithm structure or…
The outcomes of a series of measurements, made on a quantum system, form a sequence of random events which occur in a particular order. The system, together with a meter or meters, can be seen as following the paths of a stochastic network…
It is widely known that `collapse of the wave function' on a quantum system A may be brought about by an interaction with another quantum system B. We will prove that this is not just a possible, but a necessary consequence of information…
Quantum measurements are not deterministic. For this reason quantum measurements are repeated for a number of shots on identically prepared systems. The uncertainty in each measurement depends on the number of shots and the expected outcome…
The problem of measurement in quantum mechanics is reanalyzed within a general, strictly probabilistic framework (without reduction postulate). Based on a novel comprehensive definition of measurement the natural emergence of objective…
The concept of Shannon entropy of random variables was generalized to measurable functions in general, and to simple functions with finite values in particular. It is shown that the information measure of a function is related to the time…
The uncertainty principle is one of the fundamental features of quantum mechanics and plays an essential role in quantum information theory. We study uncertainty relations based on variance for arbitrary finite $N$ quantum observables. We…
Majorisation, also called rearrangement inequalities, yields a type of stochastic ordering in which two or more distributions can be compared. In this paper we argue that majorisation is a good candidate as a theory for uncertainty. We…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…
In quantum mechanics, outcomes of measurements on a state have a probabilistic interpretation while the evolution of the state is treated deterministically. Here we show that one can also treat the evolution as being probabilistic in nature…
We address the fundamental problem of selection under uncertainty by modeling it from the perspective of Bayesian persuasion. In our model, a decision maker with imperfect information always selects the option with the highest expected…
We present a quantum information theory that allows for a consistent description of entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices (rather than probability distributions) for the…