Related papers: Computational relative entropy
The von Neumann entropy is a key quantity in quantum information theory and, roughly speaking, quantifies the amount of quantum information contained in a state when many identical and independent i.i.d. copies of the state are available,…
Given an unknown quantum state distributed over two systems, we determine how much quantum communication is needed to transfer the full state to one system. This communication measures the "partial information" one system needs conditioned…
We live in the information age. Claude Shannon, as the father of the information age, gave us a theory of communications that quantified an "amount of information," but, as he pointed out, "no concept of information itself was defined."…
According to the probability ranking principle, the document set with the highest values of probability of relevance optimizes information retrieval effectiveness given the probabilities are estimated as accurately as possible. The key…
Many quantum chemical similarity measures have been derived and substantiated by applying concepts and quantities from information theory to the electron density. To justify the use of information theory, the electron density is usually…
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,…
Quantum machine learning is an emerging field at the intersection of machine learning and quantum computing. Classical cross entropy plays a central role in machine learning. We define its quantum generalization, the quantum cross entropy,…
Information theory, though originally developed for communications engineering, provides mathematical tools with broad applications across science. These tools characterize the fundamental limits of data compression and transmission in the…
The matrix-based R\'enyi's entropy allows us to directly quantify information measures from given data, without explicit estimation of the underlying probability distribution. This intriguing property makes it widely applied in statistical…
I review recent works showing that information geometry is a useful framework to characterize quantum coherence and entanglement. Quantum systems exhibit peculiar properties which cannot be justified by classical physics, e.g. quantum…
This thesis investigates the connection between quantum theory, thermodynamics and information theory. Theories with structure similar to that of quantum theory are considered, mathematically described by the framework of "Generalized…
Unitarity provides mathematical and physical constraints on quantum information systems. e.g., in entanglement swapping, unitarity requires the same von Neumann entanglement entropy generation for either a particle interaction or an act of…
Certified randomness guaranteed to be unpredictable by adversaries is central to information security. The fundamental randomness inherent in quantum physics makes certification possible from devices that are only weakly characterised, i.e.…
A fundamental approach for the characterization and quantification of all kinds of resources is to study the conversion between different resource objects under certain constraints. Here we analyze, from a resource-non-specific standpoint,…
The operational characterization of quantum coherence is the corner stone in the development of resource theory of coherence. We introduce a new coherence quantifier based on max-relative entropy. We prove that max-relative entropy of…
A framework for a quantum information theory is introduced that is based on the measure of quantum information associated with probability distribution predicted by quantum measuring of state. The entanglement between states of measured…
A method of representing probabilistic aspects of quantum systems is introduced by means of a density function on the space of pure quantum states. In particular, a maximum entropy argument allows us to obtain a natural density function…
In Coles-Piani's recent remarkable version of the entropic uncertainty principle, the entropic sum is controlled by the first and second maximum overlaps between the two projective measurements. We generalize the entropic uncertainty…
A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon)…
In this paper we deal with the problem of overcoming the intuitive definition of several color perception attributes by replacing them with novel mathematically rigorous ones. Our framework is a quantum-like color perception theory recently…