Random access codes and nonlocal resources
Anubhav Chaturvedi , Marcin Pawłowski , Karol Horodecki
AbstractThis 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.
|Journal series||Physical Review A, ISSN 1050-2947|
|Publication size in sheets||0.7|
|Score|| = 35.0, 20-12-2017, ArticleFromJournal|
= 35.0, 20-12-2017, ArticleFromJournal
|Publication indicators||: 2016 = 2.925 (2) - 2016=2.716 (5)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.