Relations for certain symmetric norms and anti-norms before and after partial trace

DOI10.1007/s10955-012-0569-8zbMath1260.81011arXiv1202.3853OpenAlexW2071339916WikidataQ62123173 ScholiaQ62123173MaRDI QIDQ690725

Alexey E. Rastegin

Publication date: 29 November 2012

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.3853

zbMATH Keywords

singular valuesTsallis entropySchatten normsymmetric anti-normsRényi entropyKy Fan norm

Mathematics Subject Classification ID

Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Quantum measurement theory, state operations, state preparations (81P15) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07) Measures of information, entropy (94A17) Open systems, reduced dynamics, master equations, decoherence (81S22) Quantum state spaces, operational and probabilistic concepts (81P16)

Related Items (12)

Separability conditions based on local fine-grained uncertainty relations ⋮ Quantum reference frames and their applications to thermodynamics ⋮ Universal Security for Randomness Expansion from the Spot-Checking Protocol ⋮ Quantum estimation through a bottleneck ⋮ Quantum reading of quantum information ⋮ Some properties of the \(k\)th-partial Rényi entropy ⋮ Landauer's principle in repeated interaction systems ⋮ Schatten q-norms and determinantal inequalities for matrices with numerical ranges in a sector ⋮ On quantum conditional entropies defined in terms of the \(F\)-divergences ⋮ A treatment of a determinant inequality of Fiedler and Markham ⋮ Extensions of some matrix inequalities related to trace and partial traces ⋮ On Uncertainty Relations and Entanglement Detection with Mutually Unbiased Measurements

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Continuity and stability of partial entropic sums
• Bounds on shannon distinguishability in terms of partitioned measures
• Some general properties of unified entropies
• The Wigner-Yanase entropy is not subadditive
• Superadditivity of Wigner-Yanase-Dyson information revisited
• Quasi-entropies for finite quantum systems
• Concavity of certain maps on positive definite matrices and applications to Hadamard products
• Completely positive linear maps on complex matrices
• On partial fidelities
• Possible generalization of Boltzmann-Gibbs statistics.
• Extensions of Lieb's concavity theorem
• Uniform estimates on the Tsallis entropies
• A continuity property of the entropy density for spin lattice systems
• Linear transformations which preserve trace and positive semidefiniteness of operators
• Convex trace functions and the Wigner-Yanase-Dyson conjecture
• Continuity bounds on the quantum relative entropy — II
• A UNIFIED TREATMENT OF CONVEXITY OF RELATIVE ENTROPY AND RELATED TRACE FUNCTIONS, WITH CONDITIONS FOR EQUALITY
• ENTROPIC CHARACTERIZATION OF QUANTUM OPERATIONS
• NORM AND ANTI-NORM INEQUALITIES FOR POSITIVE SEMI-DEFINITE MATRICES
• QUANTUM f-DIVERGENCES AND ERROR CORRECTION
• On unified-entropy characterization of quantum channels
• Continuity bounds on the quantum relative entropy
• On the stability of generalized entropies
• Matrix Analysis
• Continuity of quantum conditional information
• Distance bounds on quantum dynamics
• Unified entropy, entanglement measures and monogamy of multi-party entanglement
• Upper continuity bounds on the relative q-entropy for q > 1
• Geometry of Quantum States
• Higher entropic uncertainty relations for anti-commuting observables
• Positive Functions on C ∗ -Algebras
• Nonextensive statistical mechanics and its applications. Papers from the IMS winter school on statistical mechanics: nonextensive generalization of Boltzmann-Gibbs statistical mechanics and its applications, Okazaki, Japan, February 15--18, 1999
• Metric-adjusted skew information: convexity and restricted forms of superadditivity

This page was built for publication: Relations for certain symmetric norms and anti-norms before and after partial trace