An exfoliated monolayer CrI3 possessing the ferromagnetic (FM) nature of out-of-plane Ising spin-up (or spin-down) electrons can be considered as a qubit with a quantum state of |ѱ>=|↑>=|0> (or |ѱ>=|↓>=|1>) due to the theory of the Bloch sphere. Therefore, here a bipartite quantum system of the FM or antiferromagnetic (AFM) bilayer CrI3 is proposed for four fundamental two-qubit (2Q) quantum states (≡|ѱѱ>) of |↑↓>=|01>, |↓↑>=|10>, |↑↑>=|00> and |↓↓>=|11>, respectively. Energy-resolved magnetic circular dichroism (MCD) spectropolarimetry was used to detect d-d transitions of the FM and AFM bilayer CrI3 for the four fundamental quantum states. The obtained MCD spectra of the d-d transitions with spin-frustration and spin-parallelism possess quantum signals of the four fundamental 2Q quantum states at θB=0, where θB is the angle between the magnetic field and the surface normal. Hence, the bilayer CrI3 is a potential candidate for use in quatum computer.