First Observation of Quantum Correlations in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>e</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:mi>X</mml:mi><mml:mi>D</mml:mi><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo stretchy="true">¯</mml:mo></mml:mover></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi></mml:math>-Even Constrained <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>D</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="true">¯</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:math> Pairs

The study of meson pairs produced with quantum correlations gives direct access to parameters that are challenging to measure in other systems. In this Letter, the existence of quantum correlations due to charge-conjugation symmetry C are demonstrated in DD[over ¯] pairs produced through the processes e^{+}e^{-}→DD[over ¯], e^{+}e^{-}→D^{*}D[over ¯], and e^{+}e^{-}→D^{*}D[over ¯]^{*}, where the lack of charge superscripts refers to an admixture of neutral-charm-meson particle and antiparticle states, using 7.13 fb^{-1} of e^{+}e^{-} collision data collected by the BESIII experiment between center-of-mass energies of 4.13-4.23 GeV. Processes with either C-even or C-odd constraints are identified and separated. A procedure is presented that harnesses the entangled production process to enable measurements of D^{0}-meson hadronic parameters. This Letter provides the first confirmation of quantum correlations in e^{+}e^{-}→XDD[over ¯] processes and the first observation of a C-even constrained DD[over ¯] system. The procedure is applied to measure δ_{Kπ}^{D}, the strong phase between the D^{0}→K^{-}π^{+} and D[over ¯]^{0}→K^{-}π^{+} decay amplitudes, which results in the determination of δ_{Kπ}^{D}=(192.8_{-12.4-2.4}^{+11.0+1.9})°. The potential for measurements of other hadronic decay parameters and charm mixing with these and future datasets is also discussed.