Citation: Gao, Jingliang. "Quantum union bounds for sequential projective measurements." Physical Review A 92.5 (2015): 052331.
Web: https://arxiv.org/abs/1410.5688
Tags: Information-theory
This paper proves a very cute result, analogous to the union in classical probability theory. This result seems quite fundamental, so it is surprising that this paper came out in 2015. The proof given by the author is long and somewhat cumbersome, and is improving on earlier results by Sen and Wilde:
> Sen, Pranab. "Achieving the Han-Kobayashi inner bound for the quantum interference channel." 2012 IEEE International Symposium on Information Theory Proceedings. IEEE, 2012.
> Wilde, Mark M. "Sequential decoding of a general classical-quantum channel." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469.2157 (2013): 20130259.
This result has since been refined and improved, to the point that the proofs are now quite simple:
> Khabbazi Oskouei, Samad, Stefano Mancini, and Mark M. Wilde. "Union bound for quantum information processing." Proceedings of the Royal Society A 475.2221 (2019): 20180612.
> O'Donnell, Ryan, and Ramgopal Venkateswaran. "The quantum union bound made easy." Symposium on Simplicity in Algorithms (SOSA). Society for Industrial and Applied Mathematics, 2022.