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

Qubit state monitoring by measurement of three complementary observables