Studies On Quantum Information Processing Based On Selection After Measurement Method

Quantum information science is an interdisciplinary subject of quantum mechanics and information theory.Its research direction mainly includes quantum communication and quantum computing.Quantum communication utilizes quantum entanglement,quantum non-cloning theorem and uncertainty principle,which can achieve communication security of information theory.Quantum computing uses properties such as quantum superposition and entanglement to perform parallel computing.It has greatly enhanced the computing power,while compared with traditional computers.Both quantum communication and quantum computing involve quantum measurement.The selection after measurement is an important method for both of them.For quantum communication,the eavesdropping detection can be performed after the measurement to determine whether to retain the measurement result or the quantum state.For quantum algorithms,the selection after measurement method can be used to design nonunitary evolution operators,which enriches the designed methods of quantum algorithms.In this thesis,we conduct theoretical research on quantum communication and quantum algorithms based on the selection after measurement method.The main research results of this study includes:(1)Based on the analysis of the quantum secure direct communication protocol,a measurement-device-independent quantum secure direct communication protocol is proposed.With analyzing and selecting the measurement results of third parties,the measurement-device-independent quantum secure direct communication protocol can eliminate loopholes of quantum secure direct communication in non-ideal measurement devices in principle of the protocol.It's the first measurement-device-independent quantum secure direct communication theory in the world.This part corresponds to the second chapter of this thesis.(2)We analyzed the duality quantum computing framework based on the method of linear combination of unitaries.We gave the method to design quantum algorithms based on the selection after measurement method in the framework of duality quantum computing.We implemented HHL algorithm for solving linear systems of equations in this framework.This part corresponds to the third chapter of this thesis.(3)Based on the duality quantum computing framework,we proposed a new quantum algorithm for linear systems of equations by constructing techniques such as amplitude superposition and selection after measurement method.The quantum algorithm exhibits advantages in computational complexity compared with other quantum algorithms under certain constraints.This part corresponds to the fourth chapter of this thesis.