Resource theory of unextendibility and non-asymptotic quantum capacity

TL;DR

This paper develops a resource theory of unextendibility to analyze quantum communication limits, providing tighter bounds on quantum capacity for certain channels and revisiting the strong converse for antidegradable channels.

Contribution

It introduces a new resource theory of unextendibility, defines related quantifiers, and derives tighter non-asymptotic bounds on quantum capacity using this framework.

Findings

Tighter non-asymptotic bounds for depolarizing and erasure channels.

Establishment of upper bounds on quantum capacity for antidegradable channels.

Revisiting the strong converse for quantum capacity with new bounds.

Abstract

In this paper, we introduce the resource theory of unextendibility as a relaxation of the resource theory of entanglement. The free states in this resource theory are the k-extendible states, associated with the inability to extend quantum entanglement in a given quantum state to multiple parties. The free channels are k-extendible channels, which preserve the class of k-extendible states. We define several quantifiers of unextendibility by means of generalized divergences and establish their properties. By utilizing this resource theory, we obtain non-asymptotic upper bounds on the rate at which quantum communication or entanglement preservation is possible over a finite number of uses of an arbitrary quantum channel assisted by k-extendible channels at no cost. These bounds are significantly tighter than previously known bounds for both the depolarizing and erasure channels. Finally, we revisit the pretty strong converse for the quantum capacity of antidegradable channels and establish an upper bound on the non-asymptotic quantum capacity of these channels.