A novel measurement of the strong-phase difference between $D^0\to K^{-}{\pi }^{+}$ and ${\bar{D}}^0\to K^{-}{\pi }^{+}$ decays using $C$-even and $C$-odd quantum-correlated $D\bar{D}$ pairs

A novel measurement technique of strong-phase differences between the decay amplitudes of $D^0$ and ${\bar{D}}^0$ mesons is introduced which exploits quantum-correlated $D\bar{D}$ pairs produced by $e^{+}{e}^{-}$ collisions at energies above the $\psi (3770)$ production threshold, where $D\bar{D}$ pairs are produced in both even and odd eigenstates of the charge-conjugation symmetry. Employing this technique, the first determination of a $D^0$-$\overline{D^0}$ relative strong phase is reported with such data samples. The strong-phase difference between $D^0\to K^{-}{\pi }^{+}$ and ${\bar{D}}^0\to K^{-}{\pi }^{+}$ decays, ${\delta }_{K\pi }^D$, is measured to be ${\delta }_{K\pi }^D={\left(192.8_{-12.4-2.4}^{+11.0+1.9}\right)}^{\circ }$, using a dataset corresponding to an integrated luminosity of 7.13 ${\text{fb}}^{-1}$ collected at center-of-mass energies between $4.13-4.23\text{ GeV}$ by the BESIII experiment.