Role of nonclassical temporal correlation in powering quantum random access codes

TL;DR

This paper investigates the quantum advantage in random access codes, linking it to violations of temporal inequalities and demonstrating how such violations can certify genuine quantum randomness.

Contribution

It introduces new temporal inequalities compatible with noninvasive realism and establishes their connection to quantum advantage and randomness certification in random access codes.

Findings

Quantum advantage corresponds to violation of temporal inequalities.

Maximal success probability aligns with maximal violation of inequalities.

Violations can certify genuine quantum randomness.

Abstract

We explore the fundamental origin of the quantum advantage behind random access code. We propose new temporal inequalities compatible with noninvasive-realist models and show that any non-zero quantum advantage of n bits encoded to 1-bit random access code in the presence of shared randomness is equivalent to the violation of the corresponding temporal inequality. As an immediate consequence of this connection, we also prove that the maximal success probability of n bits encoded to 1-bit random access code can be obtained when the maximal violation of the corresponding inequality is achieved. We then show that any non-zero quantum advantage of n bits encoded to 1-bit random access code, or in other words, any non-zero violation of the corresponding temporal inequality can certify genuine randomness.