Stronger hierarchy between local quantum uncertainty and local quantum fisher information potentials

Abstract

Inspired by previous studies on entanglement potentials as measures of nonclassicality for single-mode optical states, this work introduces two novel quantifiers based on local quantum uncertainty potential (LQUP) and local quantum Fisher information potential (LQFIP). These two related potentials are employed to characterize the nonclassical nature of single-mode optical fields beyond conventional entanglement-based measures and exhibit similar trends. In particular, the relationship between LQFIP and LQUP is revealed. The exact lower and upper bounds of LQFIP versus LQUP are obtained for a specific class of nonclassical states, and the respective states which saturate those bounds are also characterized. This allows us to establish a strong hierarchy of nonclassicality for single-qubit optical states, mapped directly from the hierarchy of two-qubit quantum correlations. Our findings not only provide new tools for quantifying nonclassicality but also deepen the understanding of quantum resources in optical systems, with potential applications in quantum metrology and information processing.