Quantum Correlation Classification And Quantification For Multipartite Quantum Systems

With the development of big data technologies,the demand of computing capacity keeps continuously increasing.Quantum computing is one of the most promising tech-niques for improving the computing power of single chips.Therefore,quantum computers are regarded as the most potential candidate of next generation computing.Quantum in-formation theory is the foundation of quantum computing,thus research on quantum information theory is particularly meaningful.Among all the research directions of quantum information theory,quantum corre-lation plays vital role in both quantum communication and quantum computation.Over the past decades,quantum entanglement was considered to be the only ingredient of quantum correlation.To explicitly characterize the entanglement structure of quantum systems,researchers have proposed various approaches to classify and measure quantum entanglement.However,these approaches only take effect for quantum systems with less and low-dimensional particles.Meanwhile,they are considerably hard to be generalized to multipartite high-dimensional quantum systems.In this thesis,we have proposed a complete approach for entanglement classification by using the ranks of the coefficient matrices for arbitrary-dimensional quantum systems.We have also proposed a novel entanglement measure and found the connection between our measure and the singular values of the coefficient matrices.As researchers look deeper inside quantum systems,they have found that quantum entanglement is only a subset of quantum correlation.It has been shown that some states without entanglement can still reveal their power in quantum speed-up.For the last twenty years,researchers are looking for a quantity that measures the quantum correlation of a given quantum state.One of the famous quantifiers of quantum correlation is quantum discord.However,the calculation of quantum discord cannot walk around the complicated optimization procedure.The proposal of local quantum uncertainty partly solves this issue since the closed form of the local quantum uncertainty for 2 ×d quantum systems can be obtained.But for bipartite quantum systems with arbitrary dimensions,the complicated optimization still cannot be avoided.In this thesis,we have obtained the closed form of the lower bound of the local quantum uncertainty for arbitrary-dimensional bipartite quantum states.Our contributions are· We have proved that for multipartite arbitrary-dimensional quantum systems,the ranks of the coefficient matrices are invariant under stochastic local operation and classical communication,and proposed a complete approach for entanglement clas-sification.By using our approach,we have derived the classification results for 2×2×2× d quantum systems for the first time,and illustrated their entanglement structure by an entanglement pyramid.· We have proved the ranks of coefficient matrices are entanglement monotones.Meanwhile,we have proposed a novel entanglement measure named MAPE,and proved MAPE is an entanglement monotone.Using MAPE,we have studied the entanglement characters of several famous quantum states.We have also found the relationship between MAPE and the singular values of the coefficient matrices,which speeds up the calculation of MAPE..We have derived the closed form of the lower bound of the local quantum uncertainty.We have compared the optimized local quantum uncertainty and our lower bound for several 3×3 quantum states,the results show that our bound is tight.Meanwhile,we have studied the quantum correlation during decoherence for 3 × 3 quantum states in terms of our lower bound.