A Robust Measure Of Quantum Channel Purity

Quantum resource theories offer a highly versatile and powerful framework for studying different resource(quantum entanglement,quantum coherence,quantum non-Markov,etc.)in quantum physics.Pure state has been well applied in various quantum information processing,such as quantum teleportation,superdense coding,Shor algorithm and HHL algorithm,naturally,it can be regarded as one quantum resources.The purity measure mainly describes the degree of deviation between a quantum state and the maximally mixed state,thus how to quantitatively depict purity is a basic problem in quantum information theory.Horodecki et al.initiated the concept of purity in 2003,followed by more profound theoretical research,in 2008,Streltsov et al.proposed the axiomatic requirements for purity measure and established the purity resource theory.Furthermore,various purity measures are given depending on different measures,such as the relative entropy of purity,Renyi?-purity,the robustness of purity,and so on.Quantum resource theories can be divided into static resource theory and dynamic resource theory according to different research objects.The static resource theory corresponding to the quantum state,while the dynamic resource theory focus on the quantum channel.In fact,quantum state can also be regarded as a dynamic resource,that is dynamic resource theory enriches and develops the static resource theory.In quantum information processing,the purity of quantum states may be affected by the quantum channels,as a result,it is necessary to discuss the purity of quantum channels based on the framework of resource theory.In this thesis,the robustness measure is used to quantitatively characterize the purity of quantum channels.The relevant basic knowledge in quantum information used in this thesis is stated at the beginning,as well as the introduction of quantum coherence resource theory and the quantum purity resource theory.The traditional qualitative characterization of purity is transformed into quantitative quantification,which obtained Renyi 2-purity.Based on Renyi 2-purity,we discussed the purity power of quantum channels.Finally,the robustness of purity of quantum channels and its properties is elucidated according to the purity resource theory,besides the efficient numerical calculation of this purity measure is derived by a semidefinite programming,particularly,the numerical calculation as an application to analyze the purity of quantum channel for some single-qubit channels.