Random access codes and non-local resources
Anubhav Chaturvedi, Marcin Pawlowski, Karol Horodecki

TL;DR
This paper generalizes non-local resources and random access codes, establishing their inter-convertibility, resource inequalities, and limitations, especially for higher-dimensional inputs and messages, advancing understanding of non-locality and information processing.
Contribution
Introduces generalized non-local boxes and random access codes, analyzes their equivalences, and derives resource inequalities, extending the theoretical framework of non-local correlations.
Findings
$B_n$-BOX is equivalent to no-signaling $(n\rightarrow 1)$ RACBOX.
Signaling $(n\rightarrow 1)$ RB cannot simulate $B_n$-BOX.
Resource inequalities are saturated, quantifying the resources needed for RACs.
Abstract
It is known that a PR-BOX (PR), a non-local resource and random access code (RAC), a functionality (wherein Alice encodes 2 bits into 1 bit message and Bob learns one of randomly chosen Alice's inputs) are equivalent under the no-signaling condition. In this work we introduce generalizations to PR and RAC and study their inter-convertibility. We introduce generalizations based on the number of inputs provided to Alice, -BOX and RAC. We show that a -BOX is equivalent to a no-signaling RACBOX (RB). Further we introduce a signaling RB which cannot simulate a -BOX. Finally to quantify the same we provide a resource inequality between RB and -BOX, and show that it is saturated. As an application we prove that one requires atleast PRs supplemented with…
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