Quantum optics offer new possibilities, new approaches, and potentially groundbreaking new technologies whose backbone is based on creation, manipulation, and detection of special quantum states of light. The main objective of the thesis is to present a study of spontaneously arisen heralded entangled photon-pairs which play crucial role in emerging quantum enhanced technologies. We have mainly investigated discrete transverse-spatial-mode entangled photon-pairs in waveguide, because it intrinsically offers infinite dimension. Entangled states of higher dimensional systems enable realization of quantum information schemes that can offer higher information density coding and show more error resilience than can be achieved with lower dimensional systems. In this context, we have exploited a gradedindex optical fiber as photon-pair-generation platform via nonlinear intermodal-four-wave mixing (FWM), since the fiber may allow different FWM processes to overlap in spectral domain, resulting in an entangled pair of spatial qubits. We have also probed joint spectral properties of the generated photons to show capability of hyperentanglement in frequency and transverse mode. We have discussed spatial Wigner function and its realization to characterize spatial properties of the quantum state. We have shown that entanglement can be verified through a violation of the Clauser - Horne - Shimony - Holt (CHSH) inequality based on spatial Wigner function and coupled-mode theory. This thesis also includes basic analysis of transverse-mode entangled photon-pair distribution in a lossy-dispersive medium. Finally, the ways to follow and the quantities to measure are touched upon. Thus, we have explained the generation and four different detection schemes, relying on a combination of photon-number statistics, joint spectral properties, and spatial entanglement measurements.