English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

A natural operational paradigm for distributed quantum and classicalinformation processing involves local operations coordinated by multiple roundsof public communication. In this paper we consider the minimum number ofcommunication rounds needed to perform the locality-constrained task ofentanglement transformation and the analogous classical task of secrecymanipulation. Specifically we address whether bipartite mixed entanglement canalways be converted into pure entanglement or whether unsecure classicalcorrelations can always be transformed into secret shared randomness usinglocal operations and a bounded number of communication exchanges. Our maincontribution in this paper is an explicit construction of quantum and classicalstate transformations which, for any given $r$, can be achieved using $r$rounds of classical communication exchanges but no fewer. Our results revealthat highly complex communication protocols are indeed necessary to fullyharness the information-theoretic resources contained in general quantum andclassical states. The major technical contribution of this manuscript lies inproving lower bounds for the required number of communication exchanges usingthe notion of common information and various lemmas built upon it. We propose aclassical analog to the Schmidt rank of a bipartite quantum state which we callthe secrecy rank, and we show that it is a monotone under stochastic localclassical operations.

Round Complexity in the Local Transformations of Quantum and Classical States