Optimal Pointers for Joint Measurement of σx and σz via Homodyne Detection

• Main Authors: Bas Janssens, Luc Bouten
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Published: 2006
• Subjects: The Pointers
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.252.8934; http://arxiv.org/pdf/quant-ph/0510086v1.pdf

We study a model of a qubit in interaction with the electromagnetic field. By means of homodyne detection, the field-quadrature At+A ∗ t is observed continuously in time. Due to the interaction, information about the initial state of the qubit is transferred into 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 σx and σz. 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. 1