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In this letter, we propose a novel approach to concurrently measure thecomplementary $CP$ violation observables induced by $T$-odd correlations andtheir corresponding $T$-even counterparts, where $T$ represents time reversal.Our analysis demonstrates that $T$-odd and -even correlations, when satisfyingspecific conditions, result in cosine and sine strong phase dependencies of thecorresponding $CP$ violation, respectively. Additionally, we identify pairs ofthese $CP$ violation observables in hadron decays depend on precisely the samestrong phases within the helicity amplitude scheme. This complementarityeffectively reduces the strong phase reliance in the study of $CP$ violation,while also mitigating the risk of suppressed $CP$ violation due toexceptionally small strong phases. Furthermore, our proposal holds potentialfor uncovering $CP$ violation in baryon decays that have not yet been observedin experiments.

Complementary $CP$ violation induced by $T$-odd and $T$-even correlations