Quantum Information Measurement And Application Of Image Processing Based On Nuclear Magnetic Resonance System

Quantum information science obtained the rapid development in the last three decades and has been the subject of countless discoveries.It is based on quantum me-chanical theory,combing with mathematics,computing science and material science etc.Quantum information has many characteristics different from classical informa-tion,so it possesses great potential in information security,information storage and in-formation processing.Many problems which are unreachable for classical information,now may have solutions due to quantum information science.Quantum information technology may change our ways of information processing and achieve a leap forward to the ability of human information processing.For the quantum information process,because the object is different from the classical world,it is very important to study quantum information processing and reading.Many problems,such as how to effec-tively read the information contained in quantum states or identify the quantum chan-nels,how to understand the quantum mechanics incompatible principle's influence on quantum information,how to quickly implement necessary transformations on quantum information,are urgent for people to solve.The study of these issues will be a hot topic for a long time.In all potential physical systems which might be used to realize quan-tum information processing,nuclear magnetic resonance(NMR)system is the preferred platform for testing many quantum processing methods,depending on its relatively ma-ture control technology and long decoherence time.A lot of quantum algorithms and quantum simulations have been experimentally demonstrated in NMR system.In this thesis,I will briefly introduce the field of quantum computing based on NMR system.Focusing on the project of "Quantum Information Measurement and Application of Image Processing Based on Nuclear Magnetic Resonance System",the main contents of the thesis are divided into the following parts:Chapter 1,2.In the first two chapters,I introduce the overall background,includ-ing quantum information science and NMR quantum information processor.Chapter 3.In this chapter,I introduce two works on quantum information reading,including quantum state tomography(QST)and quantum process tomography(QPT).In the first one,we theoretically extend the method of QST by a single apparatus to n-qubit case through pairwise interactions and experimentally reconstruct 2-qubit states with this method.In the second one,we investigate QST for pure states and QPT for unitary channels via adaptive measurements.The adaptive protocols significantly reduce the number of experiments.We experimentally reconstructed the universal quantum gates with this protocol.Chapter 4.In this chapter,I introduce some studies about the uncertainty relation.We firstly consider the bipartite system with quantum memory.After a complete set of mutually unbiased bases(MUBs)measurements on one partite,we derive an uncer-tainty conservation relation,which means that the global uncertainty is a constant,just depending on the initial bipartite state.In experiment,we verify the uncertainty conser-vation relation by a directly measuring method and readout the linear entropy through a probe qubit.The second subject is about measurement uncertainty.We reformulate the existed theoretical framework and derived an improved relation based on statistical dis-tances for qubit measurement.In experiment,we test the uncertainty relation through simulating the joint measurement and directly reading out the joint probability from a probe qubit.Chapter 5.In this chapter,I discuss the issues about quantum image processing and the feature extraction.In the first work,we introduce the framework of quantum image processing.Some common quantum image transformations are exponentially speedup than classical transformations.We demonstrate the transformations in experiment.In addition,we provide a highly efficient quantum algorithm for edge detection with one single-qubit operation,which is independent of the size of the image.We successful extract the edge of an image in experiment.In the last part of this chapter,I present some of my thinking about quantum image recognition.Chapter 6.The summary and outlook.