Orthogonal and projected orthogonal matched filter detection
Signal Processing
Characterization of oblique dual frame pairs
EURASIP Journal on Applied Signal Processing
Foundations and Trends in Signal Processing
Sparse fusion frames: existence and construction
Advances in Computational Mathematics
Duals of Weighted Exponential Systems
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
| Hi-index | 754.84 |
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