Applications of position-based coding to classical communication over quantum channels

• Published in: Journal of physics. A, Mathematical and theoretical Vol. 51; no. 44; pp. 444002 - 444043
• Main Authors: Qi, Haoyu, Wang, Qingle, Wilde, Mark M
• Format: Journal Article
• Language: English
• Published: IOP Publishing 09.10.2018
• Subjects: entanglement-assisted error exponent; multiple quantum hypothesis testing; quantum simultaneous decoding
• ISSN: 1751-8113; 1751-8121
• DOI: 10.1088/1751-8121/aae290

Recently, a coding technique called position-based coding has been used to establish achievability statements for various kinds of classical communication protocols that use quantum channels. In the present paper, we apply this technique in the entanglement-assisted setting in order to establish lower bounds for error exponents, lower bounds on the second-order coding rate, and one-shot lower bounds. We also demonstrate that position-based coding can be a powerful tool for analyzing other communication settings. In particular, we reduce the quantum simultaneous decoding conjecture for entanglement-assisted or unassisted communication over a quantum multiple access channel to open questions in multiple quantum hypothesis testing. We then determine achievable rate regions for entanglement-assisted or unassisted classical communication over a quantum multiple-access channel, when using a particular quantum simultaneous decoder. The achievable rate regions given in this latter case are generally suboptimal, involving differences of Rényi-two entropies and conditional quantum entropies.