Fundamental properties of Tsallis relative entropy

Abstract

Fundamental properties for the Tsallis relative entropy in both classical and quantum systems are studied. As one of our main results, we give the parametric extension of the trace inequality between the quantum relative entropy and the minus of the trace of the relative operator entropy given by Hiai and Petz. The monotonicity of the quantum Tsallis relative entropy for the trace preserving completely positive linear map is also shown without the assumption that the density operators are invertible. The generalized Tsallis relative entropy is defined and its subadditivity is shown by its joint convexity. Moreover, the generalized Peierls-Bogoliubov inequality is also proven.

Cited by in corpus (57)

• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Quantum-coherence quantifiers based on the Tsallis relative $\alpha$-entropies
• Information theoretical properties of Tsallis entropies
• Steering criteria from general entropic uncertainty relations
• On uniqueness theorems for Tsallis entropy and Tsallis relative entropy
• On the maximum entropy principle and the minimization of the Fisher information in Tsallis statistics
• Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems
• Nonextensive triangle equality and other properties of Tsallis relative-entropy minimization
• Bounding generalized relative entropies: Nonasymptotic quantum speed limits
• Records Theory
• Quantifying the imaginarity of quantum states via Tsallis relative entropy
• On the joint convexity of the Bregman divergence of matrices
• No signaling and strong subadditivity condition for tomographic q-entropy of single qudit states
• On the Brukner-Zeilinger approach to information in quantum measurements
• Quantum Correlation with Sandwiched Relative Entropies: Advantageous as Order Parameter in Quantum Phase Transitions
• Bounds of the Pinsker and Fannes Types on the Tsallis Relative Entropy
• Geometric approach to quantum statistical inference
• Upper continuity bounds on the relative $q$-entropy for $q>1$
• Coherence quantifiers from the viewpoint of their decreases in the measurement process
• Perturbation Theory for Quantum Information
• Refined Young inequality and its application to divergences
• A generalized Fannes inequality
• An axiomatic characterization of a two-parameter extended relative entropy
• Affinity-based extension of non-extensive entropy and statistical mechanics
• Tsallis relative $\alpha$ entropy of coherence dynamics in Grover's search algorithm
• Variational representations related to Tsallis relative entropy
• A risk profile for information fusion algorithms
• Some inequalities on generalized entropies
• On Kirkwood--Dirac quasiprobabilities and unravelings of quantum channel assigned to a tight frame
• Analysing causal structures using Tsallis entropies
• Coherence dynamics in quantum algorithm for linear systems of equations
• Quantum $f$-divergence preserving maps on positive semidefinite operators acting on finite dimensional Hilbert spaces
• Quantum algorithms for matrix geometric means
• Conditions for the existence of a generalization of Rényi divergence
• Properties of a Generalized Divergence Related to Tsallis Relative Entropy
• Peierls-Bogolyubov's inequality for deformed exponentials
• Financial Portfolios based on Tsallis Relative Entropy as the Risk Measure
• Deformed entropy and information relations for composite and noncomposite systems
• Inequalities related to some types of entropies and divergences
• A fidelity measure for quantum states based on the matrix geometric mean
• Some inequalities for spectral geometric mean with applications
• Quantifying the imaginarity via different distance measures
• A two-parameter entropy and its fundamental properties
• Quantum work fluctuations versus macrorealism in terms of non-extensive entropies
• Some new Karamata type inequalities and their applications to some entropies
• Choi-Davis-Jensen's inequality without convexity
• On bounds of Tsallis relative entropy and an inequality for generalized skew information
• A characterization of the relative entropies
• Relaxation-speed crossover in anharmonic potentials
• Fano type quantum inequalities in terms of $q$-entropies
• On the $q$-generalised multinomial/divergence correspondence
• On a binary operation for positive operators
• Unified (r,s)-relative entropy
• Canonical divergence for flat $\alpha$-connections: Classical and Quantum
• Inequalities for relative operator entropies and operator means
• Geometric measures of discordlike quantum correlations based on Tsallis relative entropy
• On log-sum inequalities