Random access test as an identifier of nonclassicality

TL;DR

This paper introduces random access tests in general probabilistic theories to distinguish nonclassical features, revealing measurement incompatibility or super information storability through violations of classical bounds.

Contribution

It generalizes random access codes to random access tests applicable to any finite measurement collection in probabilistic theories, analyzing polygon theories for nonclassicality indicators.

Findings

Violation of classical bounds indicates nonclassicality.

Polygon theories show a fundamental difference between even and odd cases.

Random access tests can detect measurement incompatibility or super information storability.

Abstract

Random access codes are an intriguing class of communication tasks that reveal an operational and quantitative difference between classical and quantum information processing. We formulate a natural generalization of random access codes and call them random access tests, defined for any finite collection of measurements in an arbitrary finite dimensional general probabilistic theory. These tests can be used to examine collective properties of collections of measurements. We show that the violation of a classical bound in a random access test is a signature of either measurement incompatibility or super information storability. The polygon theories are exhaustively analyzed and a critical difference between even and odd polygon theories is revealed.