Random access codes and nonlocal resources

Anubhav Chaturvedi , Marcin Pawłowski , Karol Horodecki

Abstract

This work explores the notion of inter-convertibility between a cryptographic primitive: the random accesscode (RAC) and bipartite no-signaling nonlocal resources. To this end we introduce two generalizations of thePopescu-Rohrlich box (PR) and investigate their relation with the corresponding RACs. The first generalizationis based on the number of Alice’s input bits; we refer to it as the Bn-box. We show that the no-signaling condition imposes an equivalence between the Bn-box and the (n→1) RAC (encoding of n input bits to 1 bit of message). As an application we show that (n−1) PRs supplemented with one bit communication are necessary and sufficient to win a (n→1) RAC with certainty. Furthermore, we present a signaling instant of a perfectly working (n→1) RAC which cannot simulate theBn-box, thus showing that it is weaker than its no-signaling counterpart. For the second generalization we replace Alice’s input bits with d its (d-leveled classical systems); we call this theBd n-box. In this case the no-signaling condition is not enough to enforce an equivalence betweenthe Bd n-box and (n→1,d) RAC (encoding of n input d its to 1 dit of message); i.e., while the Bd n-box can win a(n→1,d) RAC with certainty, not all no-signaling instances of a (n→1,d) RAC can simulate the Bd n-box. We use resource inequalities to quantitatively capture these results.
Author Anubhav Chaturvedi
Anubhav Chaturvedi,,
-
, Marcin Pawłowski (FMPI / ITPA)
Marcin Pawłowski,,
- Institute of Theoretical Physics and Astrophysics
, Karol Horodecki (FMPI / II)
Karol Horodecki,,
- Institute of Informatics
Journal seriesPhysical Review A, ISSN 1050-2947, (A 35 pkt)
Issue year2017
Vol96
No2
Pages1-15
Publication size in sheets0.7
DOIDOI:10.1103/PhysRevA.96.022125
URL https://journals.aps.org/pra/pdf/10.1103/PhysRevA.96.022125
Languageen angielski
Score (nominal)35
ScoreMinisterial score = 35.0, 20-12-2017, ArticleFromJournal
Ministerial score (2013-2016) = 35.0, 20-12-2017, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 2.925 (2) - 2016=2.716 (5)
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