A Stronger Subadditivity of Entropy

Abstract

The strong subadditivity of entropy plays a key role in several areas of physics and mathematics. It states that the entropy S[ρ]= - Tr (ρ\ln ρ) of a density matrix ρ_{123} on the product of three Hilbert spaces satisfies S[ρ_{123}] - S[ρ_{23}] \leq S[ρ_{12}]- S[ρ_2]. We strengthen this to S[ρ_{123}] - S[ρ_{12}] \leq \sum_αn^α(S[ρ_{23}^α] - S[ρ_2^α]), where the n^αare weights and the ρ_{23}^αare partitions of ρ_{23}. Correspondingly, there is a strengthening of the theorem that the map A -> Tr \exp[L + \ln A] is concave. As applications we prove some monotonicity and convexity properties of the Wehrl entropy and entropy inequalities for quantum gases.

LaTeX2e, 24 pages

References in corpus (2)

• Inequalities for Quantum Entropy: A Review with Conditions for Equality
• The Thermodynamic Pressure of a Dilute Fermi Gas

Cited by in corpus (15)

• A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and Concavity
• Wehrl entropy, entropic uncertainty relations and entanglement
• The Thermodynamic Pressure of a Dilute Fermi Gas
• Another Short and Elementary Proof of Strong Subadditivity of Quantum Entropy
• Tomographic and improved subadditivity conditions for two qubits and qudit with j = 3=2
• Entropic entanglement criteria in phase space
• Subadditivity condition for spin-tomograms and density matrices of arbitrary composite and noncomposite qudit systems
• Harmonic analysis of iterated function systems with overlap
• Variational representations related to Tsallis relative entropy
• Multivariate extensions of the Golden-Thompson inequality
• Entropic inequalities and properties of some special functions
• Golden-Thompson's inequality for deformed exponentials
• Area laws and thermalization from classical entropies in a Bose-Einstein condensate
• Entropy estimation in a spin-1 Bose-Einstein condensate
• Comment on "Stronger subadditivity of entropy" by Lieb and Seiringer math-ph/0412009