Single-photon as well as polarization-correlated photon pair emission from a single semiconductor quantum dots is demonstrated. Single photon generation and single photon-pair generation with little uncorrelated multiphoton emission and the feasibility of media conversion of the quantum states between photon polarization and electron spin are fundamental functions for quantum information applications. Mutual media conversion for the angular momentum between photon polarization and electron spin is also achieved with high fidelity via positively charged exciton state without external magnetic field. This is a clear indication that the coupling of photon polarizations and electron spins keeps secured during whole processes before photon emission. Possibility of a metal-embedded structure is demonstrated with the observation of drastic enhancement of excitation and/or collection efficiency of luminescence as well as clear antibunching of photons generated from a quantum dot.