Union bound for quantum information processing
| Autor: | Oskouei, Samad Khabbazi, Mancini, Stefano, Wilde, Mark M. |
|---|---|
| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Proceedings of the Royal Society A, vol. 475, no. 2221, id 20180612, January 2019 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1098/rspa.2018.0612 |
| Popis: | In this paper, we prove a quantum union bound that is relevant when performing a sequence of binary-outcome quantum measurements on a quantum state. The quantum union bound proved here involves a tunable parameter that can be optimized, and this tunable parameter plays a similar role to a parameter involved in the Hayashi-Nagaoka inequality [IEEE Trans. Inf. Theory, 49(7):1753 (2003)], used often in quantum information theory when analyzing the error probability of a square-root measurement. An advantage of the proof delivered here is that it is elementary, relying only on basic properties of projectors, the Pythagorean theorem, and the Cauchy--Schwarz inequality. As a non-trivial application of our quantum union bound, we prove that a sequential decoding strategy for classical communication over a quantum channel achieves a lower bound on the channel's second-order coding rate. This demonstrates the advantage of our quantum union bound in the non-asymptotic regime, in which a communication channel is called a finite number of times. We expect that the bound will find a range of applications in quantum communication theory, quantum algorithms, and quantum complexity theory. Comment: v2: 23 pages, includes proof, based on arXiv:1208.1400 and arXiv:1510.04682, for a lower bound on the second-order asymptotics of hypothesis testing for i.i.d. quantum states acting on a separable Hilbert space |
| Databáze: | arXiv |
| Externí odkaz: |
|