2017/02/01 by N. D. Hari Dass, Dass, N. D. Hari, R. Rajath Krishna +3
Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1702.00347
openalex publication_date 2017/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We apply the notion of optimality of measurements for state determination(tomography) as originally given by Wootters and Fields to weak value tomography of pure states. They defined measurements to be optimal if they 'minimised' the effects of statistical errors. For technical reasons they actually maximised the state averaged information, precisely quantified as the negative logarithm of 'error volume'. In this paper we optimise both the state averaged information as well as error volumes. We prove, for Hilbert spaces of arbitrary (finite) dimensionality, that varieties of weak value measurements are optimal when the post-selected bases are mutually unbiased with respect to the eigenvectors of the observable being measured. We prove a number of important results about the geometry of state spaces when expressed through the weak values as coordinates. We derive an expression for the Kaëhler potential for the N-dimensional case with the help of which we give an exact treatment of the arbitrary-spin case.