2025/07/09 by Po-Chieh Liu, Christoph Hirche, Liu, Po-Chieh +3 · 5 citations
Computer Science · Engineering · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy #Wireless Communication Security Techniques
paper · pdf · doi:10.48550/arxiv.2507.07065
openalex publication_date 2025/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Rényi 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 Rényi divergence. Additionally, we give applications to error exponents in hypothesis testing, a new Riemann-Stieltjes type integral representation and a variational representation.