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We study a model of a two-level system (i.e. a qubit) in interaction with theelectromagnetic field. By means of homodyne detection, one field-quadrature isobserved continuously in time. Due to the interaction, information about theinitial state of the qubit is transferred into the field, thus influencing thehomodyne measurement results. We construct random variables (pointers) on theprobability space of homodyne measurement outcomes having distributions closeto the initial distributions of sigma-x and sigma-z. Using variationalcalculus, we find the pointers that are optimal. These optimal pointers arevery close to hitting the bound imposed by Heisenberg's uncertainty relation onjoint measurement of two non-commuting observables. We close the paper bygiving the probability densities of the pointers.Comment: 20 pages, 13 figures, typos corrected, reference adde

Optimal pointers for joint measurement of σxand σzvia homodyne detection

Optimal pointers for joint measurement of σ_xand σ_zvia homodyne detection