多体量子纯态纠缠测量的凹性

The Concavity of Multi-body Quantum Entanglement Measurements

在量子信息和量子计算中,量子纠缠是最主要的物理资源.本文基于两体量子纠缠测量的基础理论,讨论多体量子纯态纠缠测量的重要性质.首先,利用Schmidt分解方法得到两体量子纯态纠缠测量的凹性.其次,利用拓扑分析与不等式理论得到凸组合的多体量子纯态纠缠测量的凹性.最后,通过控制论与Schur-凸函数理论对任意两体量子纯态纠缠测量的上界进行了精确的估算.本文得到的凹性更加成功地描述了拓扑物态的Kitaev蜂巢模型中的拓扑序,扩大了问题的讨论范围,进而将应用于拓扑量子计算和量子精密测量中.

Quantum entanglement is the most important physical resource in quantum infor-mation and quantum computation.Based on the basic theory of two-body quantum entangle-ment measurement,the important properties of the entanglement measurement of multi-body quantum pure state is discussed by the topological analysis and control theory in this paper.Firstly,the concavity of entanglement measurement of two-body quantum pure states is obta-ined by Schmidt decomposition.Secondly,the concavity of the convex combination of the entanglement measurement of multi-body quantum pure states is considered by the topological analysis and inequality theory.Finally,the upper bound of two-body quantum pure states is precisely studied by the control theory and Schur convex function.The concavity is analytic and able to calculate,and the topological order of states is described more successfully in the Kitaev model.Therefore,this work is broadened to topological quantum computation and quantum precision measurement.