Kirkwood-Dirac nonclassicality advantages on quantum steering

Abstract

The Kirkwood-Dirac (KD) distribution is a vital framework in quantum state characterization, which reveals nonclassical correlations through phase-space representations. In this work, we introduce trace-norm-based measures to assess the KD-nonclassicality of quantum states and derive the corresponding trade-off relations for qubit and qutrit systems. For a bipartite state shared by Alice and Bob and a set of measurements applied by Alice, the maximum value of the totally averaged quantum resource of Bob’s states is introduced with respect to a quantum resource quantifier. When the maximum value exceeds the upper bound in a trade-off relation, the bipartite state is said to exhibit nonlocal advantages of quantum resource (NAQR). We prove that a state exhibiting NAQR, such as nonlocal advantages of KD-nonclassicality (NAKDNC), is steerable from Alice to Bob. We demonstrate that NAKDNC of Werner states exhibit much more quantum steering than quantum coherence and quantum imaginarity do and also explore NAKDNC of the two-qutrit isotropic states. These findings emerge KD-nonclassicality as an independent nonclassical resource with operational relevance in quantum information protocols.