Optimal Extensions of Resource Measures and their Applications
Abstract
We develop a framework to extend resource measures from one domain to a larger one. We find that all extensions of resource measures are bounded between two quantities that we call the minimal and maximal extensions. We discuss various applications of our framework. We show that any relative entropy (i.e. an additive function on pairs of quantum states that satisfies the data processing inequality) must be bounded by the min and max relative entropies. We prove that the generalized trace distance, the generalized fidelity, and the purified distance are optimal extensions. And in entanglement theory we introduce a new technique to extend pure state entanglement measures to mixed bipartite states.
Keywords
Cite
@article{arxiv.2006.12408,
title = {Optimal Extensions of Resource Measures and their Applications},
author = {Gilad Gour and Marco Tomamichel},
journal= {arXiv preprint arXiv:2006.12408},
year = {2020}
}
Comments
6 pages (main text) + 16 pages (supplemental material), v3, added references and a closed formula for the sandwiched or minimal quantum Renyi divergence with alpha in [0,1/2)