Eigenstate-Selective Entangled Two-Photon Absorption in Monolayer WSe${}_2$

We show that the Bell-state phase of a polarization-entangled photon pair controls the biexciton eigenstate distribution produced by entangled two-photon absorption (ETPA) in monolayer WSe${}_2$. In a frequency-nondegenerate ladder scheme, two independent valley pathways ($K$ and $K^{\mathrm{\prime }}$) share no intermediate state, so the biphoton phase sets the relative amplitude between them. Within the valley-symmetric limit this phase factorizes from the material response, and the resulting selection rule partitions the excitation among biexciton eigenstates according to the Bell-state phase $\phi$. The symmetric Bell state ($\phi =0$) selectively drives bright eigenstates, while the antisymmetric state ($\phi =\pi$) drives the exchange-dark eigenstate. No classical polarization source reproduces this $\phi$-dependent eigenstate distribution. Including valley dephasing and intervalley scattering at 4~K, the phase-scan visibility exceeds $0.97$ for broadband SPDC ($T_e\sim 100$~fs) with high source purity.