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Over the last few decades,quantum computing（QC）and quantum information processing（QIP）have exploded into a major field of physics,in terms of theory and experimentation extending towards a universal quantum computer as a lasting dream Additionally trapped-ion system is also considered as an ideal platform to investigate the quantum mechanical problems of fundamental nature,due to its decent isolation from exterior,high fidelity manipulation,measurement and extraordinary detection efficiency in consort with its extensive coherent operation timeThis thesis describes the edifice of ion trap experimental platforms for 40Ca+ and 43Ca+ions and precision measurement（PM）.The optical system for the 40Ca+has been improved and a new optical system design for 43Ca+ ions is elaborated.Low pass filter circuitry and helical resonator design,for high Q-factor and minimal harmonics,are upgraded.During my PhD study,the trap is modified,installed from initial stage,laser cooling and detection of ions are obtained after the ultra-high vacuum process.Furthermore,locking system of the 397 nm and 866 nm lasers is modified for long-term stability while instead of and basic logic gate operations and high fidelity detection of ions are realized.A time span was engaged for realization of two ions entanglement as well.Significantly,three fundamental physics problems related to QIP,QC and PM are explored and out of the three problems,two are presented in this thesis.Using a single ultracold 40Ca+ion trapped in a harmonic potential well,the quantum Landauer principle（LP）is verified which elucidates the minimum amount of heat cost involved in the deletion of a bit of information.The quantum version of LP consists of an equality encapsulating the system-environment mutual information and relative entropy related to reservoir.We have verified the LP for different reservoir temperatures and initial system correlations.Our experimental investigation substantiates an intimate link between information thermodynamics and quantum candidate systems for QIP and is helpful for better understanding of the fundamental physical limitations of irreversible logic operations at the quantum level.According to quantum physics two or more incompatible observables cannot be measured simultaneously with an absolute certainty,known as Heisenberg uncertainty relation.The different mathematical forms of uncertainty relation derived previously concern separate measurements of the two complementary observables performed on two ensembles of identically prepared quantum systems,which is conceptually different from the theme of Heisenberg’s idea of a trade-off for the errors of approximate simultaneous or successive measurements performed on the same system.In near past,Busch,Lathi and Werner（BLW）suggested a procedure for carrying out joint measurement of two incompatible observables which meet the original spirit of Heisenberg’s ideology of 1927.Following the BLW guidelines,we furnish a completely new mathematical stuff and carried out experimental evidence for joint measurement of three incompatible observables in three different orientations.We introduce a new exciting dimension i.e by scarifying accuracy of one of the three observables,the other two can be measured with an ultimate accuracy and in practice,our methods and results for the triplewise joint measurements are of more appealing characteristics in contrast to the previous investigations in the related domain and in the end a comprehensive introduction to the 43Ca+experimental setup is provided.