Experimentally Accessible Imaginarity Measure for Composite Quantum Systems

Abstract

In this work, we develop an experimentally accessible framework for quantifying imaginarity resources in composite quantum systems. We first formulate an observable‐based imaginarity measure using expectation values of antisymmetric Hermitian observables, thereby identifies the minimal observable sector required for evaluating imaginarity. By extending the trace‐norm imaginarity measure to multipartite systems, we introduce local imaginarity and imaginarity correlation to distinguish local and correlation contributions of imaginarity resources. We further establish observable representations for these quantities and investigate their evaluation using incomplete measurements through truncated measures based on the accessible antisymmetric sector. The performance of the truncated scheme is quantified by analyzing the retained observable ratio, lower‐bound recovery, and finite‐shot statistical convergence. Numerical investigations on qubit and qutrit systems demonstrate the behavior of local and correlation imaginarity in nonextremal states, higher‐dimensional systems, and under phase‐damping noise. Finally, we reveal a quantitative connection between imaginarity correlation and entanglement, derive an upper bound, and show that imaginarity correlation can serve as an experimentally accessible witness of entanglement. Our results provide an operational framework for characterizing and measuring imaginarity resources in realistic quantum systems.