Fully smooth one shot multipartite covering and decoupling of quantum states via telescoping

TL;DR

This paper introduces simplified and extended techniques for fully smooth one shot quantum state covering and decoupling, enabling new bounds and solutions for complex quantum information network problems.

Contribution

It simplifies and extends the telescoping cum mean zero decomposition technique to prove fully smooth results, leading to new bounds in quantum network information theory.

Findings

First fully smooth one shot inner bounds for network quantum information problems

Polyhedral inner bound for quantum communication over multiple access channels

Extension of telescoping technique to broader quantum state analysis

Abstract

We prove fully smooth one shot multipartite covering, aka convex split, results as well as fully smooth multipartite decoupling results for quantum states. Fully smooth one shot results for these problems were not known earlier, though the works of Cheng, Gao and Berta (arXiv:2304.12056) for convex split, and Colomer and Winter (arXiv:2304.12114) for decoupling, had made substantial progress by introducing a technique called telescoping cum mean zero decomposition of quantum states. We show that the telescoping cum mean zero decomposition technique can in fact be simplified and further extended in order to prove fully smooth decoupling and convex split results. Our techniques allow us to prove the first fully smooth one shot inner bounds for various fundamental network quantum information theory problems like e.g. the generalised Slepian Wolf problem of Anshu, Jain and Warsi (arXiv:1703.09961). We can also prove for the first time the natural polyhedral inner bound for sending quantum information over a quantum multiple access channel with limited entanglement assistance, first conjectured in Chakraborty, Nema and Sen (arXiv::2102.02187).