Information-disturbance tradeoff in quantum measurement on the uniform ensemble and on the mutually unbiased bases
| dc.creator | Barnum, Howard | |
| dc.date | 2002-05-24 | |
| dc.date.accessioned | 2026-07-07T06:04:14Z | |
| dc.date.available | 2026-07-07T06:04:14Z | |
| dc.description | I consider the tradeoff between the information gained about an initially unknown quantum state, and the disturbance caused to that state by the measurement process. I show that for any distribution of initial states, the information-disturbance frontier is convex, and disturbance is nondecreasing with information gain. I consider the most general model of quantum measurements, and all post-measurement dynamics compatible with a given measurement. For the uniform initial distribution over states, I show that the least-disturbing way of making any measurement is with conditional dynamics satisfying a generalization of the projection postulate, the ``square-root dynamics.'' Thus, procedures for achieving a point on the information-disturbance frontier may be assumed to involve such conditional dynamics. Also, the information-disturbance frontier for the uniform ensemble may be achieved with ``isotropic'' (unitarily covariant) dynamics. This results in a significant simplification of the optimization problem for calculating the tradeoff in this case, giving hope for a closed-form solution. I also show that the discrete ensembles uniform on the d(d+1) vectors of a certain set of d+1 ``mutually unbiased'' or conjugate bases in d dimensions form spherical 2-designs in CP_{d-1} when d is a power of an odd prime. This implies that many of the results of the paper apply also to these discrete ensembles. | |
| dc.description | 39 pages, LaTeX, revtex | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0205155 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0205155 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/90227 | |
| dc.subject | Quantum Physics | |
| dc.title | Information-disturbance tradeoff in quantum measurement on the uniform ensemble and on the mutually unbiased bases | |
| dc.type | text |