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.
On quan- tum Rényi entropies: A new generalization and some properti es
5 Pith papers cite this work. Polarity classification is still indexing.
5
Pith papers citing it
citation-role summary
background 2
citation-polarity summary
fields
quant-ph 5roles
background 1polarities
background 1representative citing papers
Derives generalization bounds for quantum learning via quantum and classical Rényi divergences, with a new modified sandwich quantum Rényi divergence shown to outperform the Petz version analytically and numerically.
Proves additivity of doubly minimized Petz Renyi mutual information for alpha in [1/2,2] and a novel duality plus additivity for the sandwiched version for alpha in [2/3, infinity] via Sion's minimax theorem.
The generalized quantum Stein's lemma remains valid for almost-iid states via a new continuity bound on relative entropy of entanglement with respect to quantum Wasserstein distance.
The direct exponent in binary quantum state discrimination for correlation detection equals the doubly minimized Petz Renyi mutual information for alpha in (1/2,1), while the strong converse exponent equals the doubly minimized sandwiched version for alpha in (1,infty).
citing papers explorer
-
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.
-
Generalization Bounds for Quantum Learning via R\'enyi Divergences
Derives generalization bounds for quantum learning via quantum and classical Rényi divergences, with a new modified sandwich quantum Rényi divergence shown to outperform the Petz version analytically and numerically.
-
Doubly minimized Petz and sandwiched Renyi mutual information: Properties
Proves additivity of doubly minimized Petz Renyi mutual information for alpha in [1/2,2] and a novel duality plus additivity for the sandwiched version for alpha in [2/3, infinity] via Sion's minimax theorem.
-
Robust generalized quantum Stein's lemma
The generalized quantum Stein's lemma remains valid for almost-iid states via a new continuity bound on relative entropy of entanglement with respect to quantum Wasserstein distance.
-
Doubly minimized Petz and sandwiched Renyi mutual information: Operational interpretation from binary quantum state discrimination
The direct exponent in binary quantum state discrimination for correlation detection equals the doubly minimized Petz Renyi mutual information for alpha in (1/2,1), while the strong converse exponent equals the doubly minimized sandwiched version for alpha in (1,infty).