2018/06/01 by Mark M. Wilde · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Coherent information #Generalization #Kullback–Leibler divergence #Mathematical Inequalities and Applications #Measure (data warehouse) #Quantum #Quantum channel #Quantum entanglement #Quantum information #Quantum operation #Quantum relative entropy #Sparse and Compressive Sensing Techniques #Statistical Mechanics and Entropy #cs.IT #math-ph #math.IT #math.MP #quant-ph
paper · pdf · doi:10.1109/isit.2018.8437925
published as Proceedings of the 2018 IEEE International Symposium on Information Theory, pages 2481--2485, Vail, Colorado, USA, June 2018 · 5 pages; shortened, more accessible version of arXiv:1710.10252; making publicly available due to public access mandate of US National Science Foundation and flag on Google Scholar
openalex publication_date 2018/06/01 · openalex created_date 2018/08/22 · arxiv created 2021/03/31 · arxiv updated 2021/04/01 · openalex updated_date 2026/08/05
The quantum relative entropy is a measure of the distinguishability of two quantum states, and it is a unifying concept in quantum information theory: many information measures such as entropy, conditional entropy, mutual information, and entanglement measures can be realized from it. As such, there has been broad interest in generalizing the notion to further understand its most basic properties, one of which is the data processing inequality. The quantum f-divergence of Petz is one generalization of the quantum relative entropy, and it also leads to other relative entropies, such as the Petz-Renyi relative entropies. In this contribution, I introduce the optimized quantum f-divergence as a related generalization of quantum relative entropy. I prove that it satisfies the data processing inequality, and the method of proof relies upon the operator Jensen inequality, similar to Petz's original approach. Interestingly, the sandwiched Renyi relative entropies are particular examples of the optimized f-divergence. Thus, one benefit of this approach is that there is now a single, unified approach for establishing the data processing inequality for both the Petz-Renyi and sandwiched Renyi relative entropies, for the full range of parameters for which it is known to hold. Full version of this paper is accessible at arXiv:1710.10252