Optimal Pointers for Joint Measurement of sigma-x and sigma-z via Homodyne Detection

Abstract

We study a model of a two-level system (i.e. a qubit) in interaction with the electromagnetic field. By means of homodyne detection, one field-quadrature 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 sigma-x and sigma-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.

arXiv comment20 pages, 13 figures, typos corrected, reference added

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Cited by in corpus (3)

• A quantum stochastic calculus approach to modeling double-pass atom-field coupling
• Approximate joint measurements of qubit observables
• Unifying Decoherence and the Heisenberg Principle