A sharp continuity estimate for the von Neumann entropy
By Koenraad M. R. Audenaert. 2006
278 citations recorded by the source corpus.
We derive an inequality relating the entropy difference between two quantum states to their trace norm distance, sharpening a well-known inequality due to Fannes. In our inequality, equality can be attained for every prescribed value of the trace norm distance.
Subfields: Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/949eb450811a0c78ee1c1a9c64257619bb24a413
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In Mathematical Physics
Citations in the corpus
- Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits (2022, unknown): “−∆Ssys = lnd − S(%τ) ≥ lnd − h( ), (152) T (%0, %τ) ≥ ∣T (%0, %∗) − T (%τ , %∗)∣ = ∣1 − 1/d − ∣, (153) where we use an inequality relating the entropy difference between two quantum states to their trace distance in the first line [154].”
- A Survey on Quantum Channel Capacities (2018, methodology): “Further properties of the von Neumann entropy function was studied by Audenaert in 2007 [25].”
- A Tight Uniform Continuity Bound for Equivocation (2019, background): “In conjunction, remarkable progress has been made in the study of the continuity of the von Neumann entropy, or matrix entropy, versus trace distance [4], [5], [6].”
- Stability of Frustration-Free Hamiltonians (2011, unknown): “Combined with the bound S(ρo(A)) ≤ (|A(`)| − |A|) lnD ≤ cd (1 + r) d−1` lnD, for ` ≤ r and cd a constant depending only on d, we have: S(ρA) ≤ S(ρ0(A)) + |S(ρA)− S(ρ0(A))| ≤ cd lnD (1 + r)d−1`+ c′′ d lnD∆0(`) (1 + r) +H(∆0(`)), (7) where we used the Fannes-Audenaert inequality [2, 12] for the entrop”