2002/05/24 by Howard Barnum, Barnum, Howard · 3 citations
Computer Science · Physics and Astronomy · #Coding theory and cryptography #Cryptography and Data Security #Cryptography and Residue Arithmetic #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0205155
39 pages, LaTeX, revtex
arxiv created 2002/05/24 · openalex publication_date 2002/05/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 CPd-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.