Information-disturbance tradeoff in quantum measurement on the uniform ensemble and on the mutually unbiased bases

Details Information-disturbance tradeoff in quantum measurement on the uniform ensemble and on the mutually unbiased bases Information-disturbance tradeoff in quantum measurement on the uniform ensemble and on the mutually unbiased bases

2002-05-24

arxiv.org/abs/quant-ph/0205155v1

Physics

Quantum Physics

39 pages, LaTeX, revtex

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Information-disturbance tradeoff in quantum measurement on the uniform ensemble and on the mutually unbiased bases does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Information-disturbance tradeoff in quantum measurement on the uniform ensemble and on the mutually unbiased bases, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Information-disturbance tradeoff in quantum measurement on the uniform ensemble and on the mutually unbiased bases will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-421389