Entanglement spread and clean resource inequalities

TL;DR

This paper investigates the challenges of entanglement spread in quantum states and protocols, revealing fundamental quantum limitations and proposing new bounds and extensions for quantum information processing.

Contribution

It introduces the concept of entanglement spread, discusses its implications, and presents new bounds and methods for quantum communication and resource inequalities.

Findings

Entanglement cannot be conditionally discarded without communication or decoherence.

Creating n partially entangled states from singlets requires theta(sqrt(n)) communication.

A new lower bound technique for quantum communication complexity.

Abstract

This article will examine states that superpose different amounts of entanglement and protocols that run in superposition but generate or consume different amounts of entanglement. In both cases we find a uniquely quantum difficulty: entanglement cannot be conditionally discarded without either using communication or causing decoherence. I will first describe the problem of entanglement spread in states and operations, as well as some methods of dealing with it. Then I'll describe three applications to problems that at first glance appear to be quite different: first, a reinterpretation of the old observation that creating n partially entangled states from singlets requires theta(sqrt(n)) communication, but cannot itself be used to communicate; second, a new lower bound technique for communication complexity; third, an explanation of how to extend the quantum reverse Shannon theorem from tensor power sources to general sources.