Optimal Tight Frames and Quantum Measurement
| dc.creator | Eldar, Y. C. | |
| dc.creator | Forney Jr, G. David | |
| dc.date | 2001-06-13 | |
| dc.date.accessioned | 2026-07-07T06:02:15Z | |
| dc.date.available | 2026-07-07T06:02:15Z | |
| dc.description | 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 (POVMs) on that space. Using this relationship, frame-theoretical analogues of various quantum-mechanical concepts and results are developed. The analogue 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 free (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. Finally, the canonical frame vectors corresponding to a geometrically uniform vector set are shown to be geometrically uniform and to have the same symmetries as the original vector set. | |
| dc.description | Submitted to IEEE Transactions on Information Theory. LaTex, 50 pages | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0106070 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0106070 | |
| dc.identifier | IEEE Trans. Inform. Theory, vol. 48, pp. 599-610, Mar. 2002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/89538 | |
| dc.subject | Quantum Physics | |
| dc.title | Optimal Tight Frames and Quantum Measurement | |
| dc.type | text |