Get started
Work

Uhlmann’s Theorem for Measured Divergences

Year: 2025
Type: article
Abstract: Uhlmann’s theorem is a cornerstone of quantum information theory, stating that for any quantum state ρABand any state σA, there exists an extension σABof σAsuch that the fidelity between ρABand σABequals the fidelity between their marginals ρAand σA. This property underpins many results and applications in quantum information science. In this work, we generalize Uhlmann’s theorem to a broad class of measuredf-divergences, including the measured α-Rényi divergences for all α ≥ 0. The well-known Uhlmann’s theorem for the fidelity corresponds to the special case α = 1/2. Since most commonly used quantum Rényi divergences, including the Petz and sandwiched Rényi divergences, cannot satisfy this property (except for degenerate cases), this fundamentally distinguishes measuredf-divergences from other quantum divergences and highlights their unique mathematical structure.
DOI: 10.1109/tit.2025.3649040
Institutions: Chinese University of Hong Kong, Shenzhen, University of Cambridge, Lyon 1 Université, École Normale Supérieure de Lyon, Institut national de recherche en sciences et technologies du numérique, Laboratoire de l'Informatique du Parallélisme
Language: English
Open Access status: green
Funders: Government of the United Kingdom, UK Research and Innovation, European Commission, Agence Nationale de la Recherche, National Natural Science Foundation of China, Shenzhen Fundamental Research Program, HORIZON EUROPE Framework Programme, European Research Council
Awards: G1171162939, G1190173965, G1204051771, G1583853050, G2330084786, G434337789, G5388051471, G5508686167, QuantERA II ERA-NET Cofund in Quantum Technologies, Distribution Quantique de clés avec des boites noires, G7362582964, G8786121556
OpenAlex ID: W4407425875
FWCI: 0.809
Cites: 32
Cited by: 2
Related to: 10