Extendibility limits the performance of quantum processors

TL;DR

This paper introduces the resource theory of unextendibility to quantify limitations on quantum entanglement extension, providing tighter bounds on quantum communication rates over certain channels.

Contribution

It develops a new resource theory of unextendibility and derives non-asymptotic bounds on quantum communication rates that outperform previous bounds.

Findings

Tighter upper bounds on quantum communication over depolarizing channels.

Tighter bounds on quantum communication over erasure channels.

Introduction of the resource theory of unextendibility.

Abstract

Resource theories in quantum information science are helpful for the study and quantification of the performance of information-processing tasks that involve quantum systems. These resource theories also find applications in other areas of study; e.g., the resource theories of entanglement and coherence have found use and implications in the study of quantum thermodynamics and memory effects in quantum dynamics. In this paper, we introduce the resource theory of unextendibility, which is associated to the inability of extending quantum entanglement in a given quantum state to multiple parties. The free states in this resource theory are the k-extendible states, and the free channels are k-extendible channels, which preserve the class of k-extendible states. We make use of this resource theory to derive non-asymptotic, upper bounds on the rate at which quantum communication or entanglement preservation is possible by utilizing an arbitrary quantum channel a finite number of times, along with the assistance of k-extendible channels at no cost. We then show that the bounds obtained are significantly tighter than previously known bounds for quantum communication over both the depolarizing and erasure channels.