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Coupled Ito equations of continuous quantum state measurement, and estimation
We discuss a non-linear stochastic master equation that governs the
time-evolution of the estimated quantum state. Its differential evolution
corresponds to the infinitesimal updates that depend on the time-continuous
measurement of the true quantum state. The new stochastic master equation
couples to the two standard stochastic differential equations of
time-continuous quantum measurement. For the first time, we can prove that the
calculated estimate almost always converges to the true state, also at
low-efficiency measurements. We show that our single-state theory can be
adapted to weak continuous ensemble measurements as well.Comment: 5 pages, RevTeX4. In version v2 some minor revisions and
clarifications have been incorporated. Moreover, a new reference has been
included. Accepted for publication in Journal of Physics A: Mathematical and
Genera