Coupled Ito equations of continuous quantum state measurement, and estimation

Abstract

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.

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 General

References in corpus (6)

• Continuous quantum measurement and Itô formalism
• Quantum state reconstruction via continuous measurement
• State determination in continuous measurement
• Feedback cooling of atomic motion in cavity QED
• Density matrix purification due to continuous quantum measurement
• Advancement of estimation fidelity in continuous quantum measurement

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