Optimal trace inequalities are derived for single-shot quantum information, replacing prior constants with a smaller Lambert-W prefactor for logarithmic traces and providing optimal two-sided collision-divergence bounds.
Layer Cake Representations for Quantum Divergences
7 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Defining suitable quantum extensions of classical divergences often poses a challenge due to the non-commutative nature of quantum information. In this work, we propose a new approach via what we call the layer cake representation. The resulting quantum R\'enyi and $f$-divergences are then proven to be equivalent to those recently defined via integral representations. Nevertheless, the approach can provide several insights. We give an alternative proof of the integral representation of the relative entropy by Frenkel and prove a conjecture regarding a trace expression for the R\'enyi divergence. Additionally, we give applications to error exponents in hypothesis testing, a new Riemann-Stieltjes type integral representation and a variational representation.
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2026 7representative citing papers
The f_0-divergence defined via Jordan decomposition integrals coincides with Araki's relative entropy on arbitrary von Neumann algebras, extending Frenkel's finite-dimensional formula.
Quantum relative entropy is the unique normalized, additive, Lorenz-continuous divergence monotone under binary guessing games.
Establishes dimension-free one-shot pairwise bounds for multiple quantum hypothesis testing, resolves Audenaert-Mosonyi conjecture, and proves achievability of multiple quantum Chernoff distance for arbitrary separable Hilbert spaces.
Minimal sufficient Jordan algebras characterize sufficiency for positive trace-preserving maps on quantum states, with Neyman-Pearson tests generating them and equality in data-processing inequalities implying Petz recovery.
Explicit formulas are given for regularized Rényi divergences of several kinds between fermionic quasifree states, with all types coinciding in the single-mode case and remaining distinct for multiple modes per site.
Quantum hockey stick f-divergences are extended to general von Neumann algebras, with regularized Rényi versions shown to coincide with standard Petz and sandwiched Rényi divergences.
citing papers explorer
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Optimal Trace Inequalities for Single-Shot Quantum Information
Optimal trace inequalities are derived for single-shot quantum information, replacing prior constants with a smaller Lambert-W prefactor for logarithmic traces and providing optimal two-sided collision-divergence bounds.
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Integral representations of $f$-divergences for general von Neumann algebras
The f_0-divergence defined via Jordan decomposition integrals coincides with Araki's relative entropy on arbitrary von Neumann algebras, extending Frenkel's finite-dimensional formula.
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Quantum Noncommutativity Uniquely Determines Relative Entropy
Quantum relative entropy is the unique normalized, additive, Lorenz-continuous divergence monotone under binary guessing games.
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Multiple Quantum Hypothesis Testing: One-Shot Pairwise Bounds and Sharp Asymptotics
Establishes dimension-free one-shot pairwise bounds for multiple quantum hypothesis testing, resolves Audenaert-Mosonyi conjecture, and proves achievability of multiple quantum Chernoff distance for arbitrary separable Hilbert spaces.
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Sufficiency and Petz recovery for positive maps
Minimal sufficient Jordan algebras characterize sufficiency for positive trace-preserving maps on quantum states, with Neyman-Pearson tests generating them and equality in data-processing inequalities implying Petz recovery.
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R\'enyi divergences and binary state discrimination error exponents for fermionic quasi-free states
Explicit formulas are given for regularized Rényi divergences of several kinds between fermionic quasifree states, with all types coinciding in the single-mode case and remaining distinct for multiple modes per site.
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Hockey stick $f$-divergences
Quantum hockey stick f-divergences are extended to general von Neumann algebras, with regularized Rényi versions shown to coincide with standard Petz and sandwiched Rényi divergences.