Qubit state monitoring by measurement of three complementary observables

Abstract

We consider the evolution of a spin 1/2 (qubit) under the simultaneous continuous measurement of three non-commuting qubit operators sigma_x, sigma_y, sigma_z. For identical ideal detectors the qubit state evolves by approaching a pure state with a random direction in the Bloch vector space and by undergoing locally isotropic diffusion in the perpendicular directions. The quantum state conditioned on the complete detector record is used to assess the fidelity of classically inspired estimates based on running time averages and discrete time bin detector outputs.

5 pages, 4 figures

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• How to perform the coherent measurement of a curved phase space by continuous isotropic measurement. I. Spin and the Kraus-operator geometry of $\mathrm{SL}(2,\mathbb{C})$
• Simultaneous Measurements of Noncommuting Observables. Positive Transformations and Instrumental Lie Groups
• Memory effects in a sequence of measurements of non-commuting observables
• Quantum feedback for measurement and control