Quantum discord in quantum random access codes and its connection with dimension witness

TL;DR

This paper investigates quantum discord in quantum random access codes (QRACs), revealing nonzero discord despite no entanglement, and explores its relationship with dimension witnesses, suggesting a fundamental link between nonclassical correlations and quantum dimension certification.

Contribution

It demonstrates that quantum discord characterizes quantum correlations in QRACs and establishes a monotonic relationship between discord and dimension witnesses, providing new insights into quantum correlations without entanglement.

Findings

Quantum discord is nonzero in QRACs without entanglement.

Quantum discord and dimension witness are monotonically related.

Quantum discord can serve as a figure of merit for QRACs.

Abstract

We exploit quantum discord (and geometric discord) to detect quantum correlations present in a well-known communication model called quantum random access codes (QRACs), which has a variety of applications in areas ranging form quantum communication complexity, network coding, information causality, to security proof of QKD protocol. In spite of the fact that there is no entanglement between the two parts involved in this model, analytical derivation shows that the quantum discord is nonzero and highlights that quantum discord might be regarded as a figure of merit to characterize the quantum feature of QRACs, since this model has no classical counterparts. To gain further insight, we also investigate the dynamical behavior of quantum discord under state rotations. As a comparison, the connection between quantum discord and dimension witness is graphically discussed. Interestingly, our results illustrate that these two quantities are monotonically related to each other, which implies that the dimension witness and nonclassical correlations may be intrinsically linked.