Research On The Reversibility Of Quantum Entanglement Operations And The Dynamic Evolution Of Quantum Purity

Quantum entanglement and quantum purity are widely used in quantum infor-mation.How to measure these quantum features has been very popular in quan-tum information,entanglement cost and distillable entanglement are fundamental measures for quantum entanglement.The reversibility of entanglement operations means that distillable entanglement is equal to entanglement cost.The asymptotic reversibility of a class of operations will lead to a unique measure of entanglement as well as the unique ordering is provided for some entangled states,and lay the foundation for classifying the states.On the other hand,quantum purity as an important quantum feature,has many similar properties with coherence and en-tanglement.Since quantum purity will have influence on transmission of quantum information,it is necessary to study the evolution of purity in quantum channels.In this thesis,we study the reversibility of entanglement operations and the evolution of purity in quantum channels,the main work is as follows:1.Using semidefinite programming(SDP),we find the reversibility for a class of states under the operations completely preserving positivity of partial transpose(PPT).At the saie time,we also prove that a]ower bound E?(?))for the asymp-totic PPT-relative entropy of entanglement is equal to the regularized Rains' bound and an upper bound EN(?)for distillable entanglement,and the specific amount of distillable entanglement and entanglement cost under PPT operations for these states are given.2.We give the definitions of purity power and de-purity power.Based on Renyi ?-Purity,we study the purity power and de-purity power of quantum chan-nels and prove that de-purity power is nonincreasing with a increasing and purity power is nondecreasing with ? increasing while there exist p for a quantum channel make every measure obtain the maximum of de-purity power.