2005/10/31 by Bas Janssens, Luc Bouten
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Direct-conversion receiver #Discrete mathematics #Homodyne detection #Joint probability distribution #Mathematics #Observable #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Qubit #Sigma #Statistical physics #Statistics #quant-ph
paper · pdf · doi:10.1088/0305-4470/39/11/013
published as J. Phys. A: Math. Gen. 39 (2006) 2773-2790 · 20 pages, 13 figures, typos corrected, reference added
arxiv created 2006/01/31 · openalex publication_date 2006/03/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study a model of a qubit in interaction with the electromagnetic field. By means of homodyne detection, the field-quadrature A t + A * t is observed continuously in time. Due to the interaction, information about the initial state of the qubit is transferred to the field, thus influencing the homodyne measurement results. We construct random variables (pointers) on the probability space of homodyne measurement outcomes having distributions close to the initial distributions of σ x and σ z . Using variational calculus, we find the pointers that are optimal. These optimal pointers are very close to hitting the bound imposed by Heisenberg's uncertainty relation on joint measurement of two non-commuting observables. We close the paper by giving the probability densities of the pointers.