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We exploit the angular and quantum correlations in the $D\bar{D}$ pairsproduced through the decay of the $\psi(3770)$ resonance in a charm factory toinvestigate CP-violation in two different ways. We consider the case of$\psi(3770)\rightarrow D\bar{D}\rightarrow (V_1V_2)(K\pi)$ decays, whichprovide a new way to measure the strong phase difference $\delta$ betweenCabibbo-favored and doubly-Cabibbo suppressed $D$ decays required in thedetermination of the CKM angle $\gamma$. We also build CP-violating observablesin $\psi(3770)\rightarrow D\bar{D}\rightarrow (V_1V_2)(V_3 V_4)$ to isolatespecific new physics effects in the charm sector. Neglecting the systematics,we give a first rough estimate of the sensitivities of these measurements atBES-III with an integrated luminosity of 20 fb$^{-1}$ at $\psi(3770)$ peak andat a future super $\tau$-charm factory with a luminosity of $10^{35}$cm$^{-2}$s$^{-1}$

Extracting strong phase and $CP$ violation in $D$ decays by using  quantum correlations in $\psi(3770)\to D^0 \overline{D}^0 \to (V_1V_2)(K  \pi)$ and $\psi(3770)\to D^0\overline{D}^0\to (V_1V_2)(V_3V_4)