This chapter deals with an estimation theory of quantum particles and systems. The estimation of all parameters has been encoded in quantum state and processed through a quantum information matrix. The researchers have used the Born-Markov approximation for quantum estimation. Quantum mechanics has proven to be a valuable resource for the investigation of the behavior of complex networks. With the arrival of quantum computers, new algorithms have come out to do quantum chemistry, and importantly, atomic-like orbitals. Quantum compression algorithms help to develop the landscape of emerging IT technologies, IoT and Internet. Quantum Image processing (QIMP) has become a popular area of quantum research due to the ubiquity and primacy of digital image and video processing in modern life. In modeling noise in the quantum circuits, we assume a model by which each one- and two-qubit gates are followed by a depolarizing noise channel. Quantum computing (QC) potential use in High Energy Physics has led CERN, one of the top world users of large-scale distributed computing, to start programs such as the Quantum Technology Initiative (QTI) to further assess and explore the applications of QC. This chapter gives a survey on quantum cryptography in which quantum key distribution protocols are proven secure for industrial applications.