Optimal tight frames and quantum measurement

被引:90
作者
Eldar, YC [1 ]
Forney, GD
机构
[1] MIT, Elect Res Lab, Cambridge, MA 02139 USA
[2] MIT, Informat & Decis Syst Lab, Cambridge, MA 02139 USA
关键词
canonical frames; least-squares frame; least-squares quantum measurement; Neumark's theorem; tight frames;
D O I
10.1109/18.985949
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
Tight frames and rank-one quantum measurements are shown to be intimately related. In fact, the family of normalized tight frames for the space in which a quantum-mechanical system lies is precisely the family of rank-one generalized quantum measurements on that space. Using this relationship, frame-theoretical analogs of various quantum-mechanical concepts and results are developed. The analog of a least-squares quantum measurement is a tight frame that is closest in a least-squares sense to a given set of vectors. The least-squares tight frame is found for both the case in which the scaling of the frame is specified (constrained least-squares frame (CLSF)) and the case in which the scaling is chosen to minimize the least-squares error (unconstrained least-squares frame (ULSF)). The well-known canonical frame is shown to be proportional to the ULSF and to coincide with the CLSF with a certain scaling.
引用
收藏
页码:599 / 610
页数:12
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