Related papers: Unpredictability, information, and chaos
The outcome of all time series cannot be forecast, e.g. the flipping of a fair coin. Others, like the repeated {01} sequence {010101...} can be forecast exactly. Algorithmic information theory can provide a measure of forecastability that…
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
We present graphs of information versus disturbance for general quantum measurements of completely unknown states. Each piece of information and disturbance is quantified by two measures: (i) the Shannon entropy and estimation fidelity for…
Measurement incompatibility describes two or more quantum measurements whose expected joint outcome on a given system cannot be defined. This purely non-classical phenomenon provides a necessary ingredient in many quantum information tasks…
General characterizations of physical measurements are discussed within the framework of the classical information theory. The uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…
Prediction is a fundamental objective of science. It is more difficult for chaotic and complex systems like turbulence. Here we use information theory to quantify spatial prediction using experimental data from a turbulent soap film. At…
We formulate the conditions under which the dynamics of a continuously measured quantum system becomes indistinguishable from that of the corresponding classical system. In particular, we demonstrate that even in a classically chaotic…
The complexity of the operating environment and required technologies for highly automated driving is unprecedented. A different type of threat to safe operation besides the fault-error-failure model by Laprie et al. arises in the form of…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
Using semiclassical methods, it is possible to construct very accurate approximations in the short wavelength limit of quantum dynamics that rely exclusively on classical dynamical input. For systems whose classical realization is strongly…
The notion of the quantum angle is introduced. The quantum angle turns out to be a metric on the set of physical states of a quantum system. Its kinematics and dynamics is studied. The certainty principle for quantum systems is formulated…
There is a fundamental limit to what is knowable about atomic and molecular scale systems. This fuzziness is not always due to the act of measurement. Other contributing factors include system parameter uncertainty, functional uncertainty…
Recent philosophical discussions about metaphysical indeterminacy have been substantiated with the idea that quantum mechanics, one of the most successful physical theories in the history of science, provides explicit instances of worldly…
Measurement uncertainty is an important topic in the undergraduate laboratory curriculum. Previous research on student thinking about experimental measurement uncertainty has focused primarily on introductory-level students' procedural…
Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion…
Quantum typicality refers to the phenomenon that the expectation values of any given observable are nearly identical for the overwhelming majority of all normalized vectors in a sufficiently high-dimensional Hilbert (sub-)space. As a…
Forecasting is usually framed as a problem of model choice. This paper starts earlier, asking how much predictive information is available at each horizon. Under logarithmic loss, the answer is exact: the mutual information between the…
We examine whether the chaotic behavior of classical systems with a limited number of degrees of freedom can produce quantum dephasing, against the conventional idea that dephasing takes place only in large systems with a huge number of…
We study information measures in quantu mechanics, with particular emphasis on providing a quantification of the notions of classicality and predictability. Our primary tool is the Shannon - Wehrl entropy I. We give a precise criterion for…