Related papers: Left-Right Relative Entropy
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
In this article we study relationship between three measures of distinguishability of quantum states called as divergence, relative entropy and the substate property.
We obtain formulas for Petz-R\'enyi and Umegaki relative entropy from the idea of distribution of a positive selfadjoint operator. Classical results on R\'enyi and Kullback-Leibler divergences are applied to obtain new results and new…
Various measures have been suggested recently for quantifying the coherence of a quantum state with respect to a given basis. We first use two of these, the l_1-norm and relative entropy measures, to investigate tradeoffs between the…
In statistical physics, if we successively divide an equilibrium system into two parts, we will face a situation that, within a certain length $\xi$, the physics of a subsystem is no longer the same as the original system. Then the…
Over the last few years, machine learning unlocked previously infeasible features for compression, such as providing guarantees for users' privacy or tailoring compression to specific data statistics (e.g., satellite images or audio…
Certain duality of relative entropy can fail for chiral conformal net with nontrivial representations. In this paper we quantify such statement by defining a quantity which measures the failure of such duality, and identify this quantity…
Quantum filtering is a signal processing technique that estimates the posterior state of a quantum system under continuous measurements and has become a standard tool in quantum information processing, with applications in quantum state…
The quantum relative entropy is frequently used as a distance measure between two quantum states, and inequalities relating it to other distance measures are important mathematical tools in many areas of quantum information theory. We have…
Extending our previous work, we study the relative entropy between the reduced density matrices obtained from globally excited states in conformal field theories of arbitrary dimensions. We find a general formula in the small subsystem size…
Partition functions of quantum critical systems, expressed as conformal thermal tensor networks, are defined on various manifolds which can give rise to universal entropy corrections. Through high-precision tensor network simulations of…
In this thesis, we study aspects of entanglement theory of quantum field theories from an algebraic point of view. The main motivation is to gain insights about the general structure of the entanglement in QFT, towards a definition of an…
We introduce and apply Hilbert's projective metric in the context of quantum information theory. The metric is induced by convex cones such as the sets of positive, separable or PPT operators. It provides bounds on measures for statistical…
Entropy is a fundamental concept in quantum information theory that allows to quantify entanglement and investigate its properties, for example its monogamy over multipartite systems. Here, we derive variational formulas for relative…
Uncertainty relations and quantum entanglement are pivotal concepts in quantum theory. Beyond their fundamental significance in shaping our understanding of the quantum world, they also underpin crucial applications in quantum information…
This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography. We investigate the conditional min- and max-entropy for quantum states, generalizations of classical R\'enyi…
Finding the minimal relative entropy of two quantum states under semidefinite constraints is a pivotal problem located at the mathematical core of various applications in quantum information theory. An efficient method for providing…
This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine…
We develop a unified, information theoretic interpretation of the number-phase complementarity that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscillator) systems. The relevant uncertainty principle is…
The quantum relative entropy is a measure of the distinguishability of two quantum states, and it is a unifying concept in quantum information theory: many information measures such as entropy, conditional entropy, mutual information, and…