A Straightforward Introduction to Continuous Quantum Measurement
arXiv:quant-ph/0611067 · doi:10.1080/00107510601101934
Abstract
We present a pedagogical treatment of the formalism of continuous quantum measurement. Our aim is to show the reader how the equations describing such measurements are derived and manipulated in a direct manner. We also give elementary background material for those new to measurement theory, and describe further various aspects of continuous measurements that should be helpful to those wanting to use such measurements in applications. Specifically, we use the simple and direct approach of generalized measurements to derive the stochastic master equation describing the continuous measurements of observables, give a tutorial on stochastic calculus, treat multiple observers and inefficient detection, examine a general form of the measurement master equation, and show how the master equation leads to information gain and disturbance. To conclude, we give a detailed treatment of imaging the resonance fluorescence from a single atom as a concrete example of how a continuous position measurement arises in a physical system.
24 pages, 3 eps figues. To appear in Contemporary Physics
References in corpus (7)
- Quantum Feedback Control of Atomic Motion in an Optical Cavity
- Squeezing of a nanomechanical resonator by quantum nondemolition measurement and feedback
- Robust quantum parameter estimation: coherent magnetometry with feedback
- Feedback cooling of atomic motion in cavity QED
- Continuous Quantum Measurement and the Quantum to Classical Transition
- The transition to classical chaos in a coupled quantum system through continuous measurement
- Persistent Entanglement in the Classical Limit
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