根据经典领域中的有限维紧框架研究量子领域中紧框架构造方法.由于紧框架与秩-广义量子测量有一一对应关系,在量子领域中设计了两种基于量子广义测量的紧框架构造方法.研究表明,这两种最优量子紧框架能分别解决两种基本的量子态区分策略:最小差错区分和最优无错区分.最小差错区分给定的一组向量,应用最小二乘准则,用广义量子测量方法构造了基于最小二乘测量(LSM)的最优量子紧框架.这种最优量子紧框架分为两种情况:一种是给定框架界的最小二乘框架(CLSF),另一种是选择最优框架界的最小二乘框架(ULSF),最优框架界能最小化最小二乘误差.用量子广义测量方法构造了基于最优无错区分的量子紧框架.最后举例对比了以上最优紧框架构造方法, ULSF为最优有限维紧框架.
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