Related papers: Purity results for some arithmetically defined mea…
We continue our study of the dynamics of mappings with small topological degree on (projective) complex surfaces. Previously, under mild hypotheses, we have constructed an ergodic ``equilibrium'' measure for each such mapping. Here we study…
For control systems in discrete time, this paper discusses measure-theoretic invariance entropy for a subset Q of the state space with respect to a quasi-stationary measure obtained by endowing the control range with a probability measure.…
In this paper we study mutual absolute continuity and singularity of probability measures on the path space which are induced by an isotropic stable L\'evy process and the purely discontinuous Girsanov transform of this process. We also…
The goal of quantum metrology is to improve measurements' sensitivities by harnessing quantum resources. Metrologists often aim to maximize the quantum Fisher information, which bounds the measurement setup's sensitivity. In studies of…
Projective measurement can increase the entropy of a state $\rho$, the increased entropy is not only up to the basis of projective measurement, but also has something to do with the properties of the state itself. In this paper we define…
The representation of a given quantity with less information is often referred to as `quantization' and it is an important subject in information theory. In this paper, we have considered absolutely continuous probability measures on unit…
In this paper, we investigate the computability of $\mathcal{G}$-Bernoulli measures, with a particular focus on measures of maximal entropy (MMEs) on coded shift spaces. Coded shifts are natural generalizations of sofic shifts and are…
We generalize previously proposed conditions each measure of entanglement has to satisfy. We present a class of entanglement measures that satisfy these conditions and show that the Quantum Relative Entropy and Bures Metric generate two…
We establish the theoretical framework for implementing the maximumn entropy on the mean (MEM) method for linear inverse problems in the setting of approximate (data-driven) priors. We prove a.s. convergence for empirical means and further…
The accuracy of a measurement of the spin direction of a spin-s particle is characterised, for arbitrary half-integral s. The disturbance caused by the measurement is also characterised. The approach is based on that taken in several…
Many experiments in quantum information aim at creating graph states. Quantifying the purity of an experimentally achieved graph state could in principle be accomplished using full-state tomography. This method requires a number of…
Entanglement and coherence are fundamental properties of quantum systems, promising to power near future quantum technologies, such as quantum computation, quantum communication and quantum metrology. Yet, their quantification, rather than…
We show that a certain type of quasi finite, conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also construct a conservative, ergodic, measure preserving…
We present the results of an operational use of experimentally measured optical tomograms to determine state characteristics (purity) avoiding any reconstruction of quasiprobabilities. We also develop a natural way how to estimate the…
We prove that the quantum trajectory of repeated perfect measurement on a finite quantum system either asymptotically purifies, or hits upon a family of `dark' subspaces, where the time evolution is unitary.
We look at the maximal entropy (MME) measure of the boundaries of connected components of the Fatou set of a rational map of degree greater than or equal to 2. We show that if there are infinitely many Fatou components, and if either the…
We present exact results for two complementary measures of spatial structure generated by 1D spin systems with finite-range interactions. The first, excess entropy, measures the apparent spatial memory stored in configurations. The second,…
We classify complex projective surfaces with an automorphism of positive entropy for which the unique invariant measure of maximal entropy is absolutely continuous with respect to Lebesgue measure.
Ergotropy -- the maximal amount of unitarily extractable work -- measures the ``charge level'' of quantum batteries. We prove that in large many-body batteries ergotropy exhibits a concentration of measure phenomenon. Namely, the ergotropy…
We identify the optimal measurement for obtaining information about the original quantum state after the state to be measured has undergone partial decoherence due to noise. We quantify the information that can be obtained by the…