A straightforward introduction to continuous quantum measurement

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.

Acknowledgments

The authors would like to thank Tanmoy Bhattacharya, Michael Raymer, Elizabeth Schoene, and Jeremy Thorn for insightful comments and corrections. DAS acknowledges support from the National Science Foundation, and KJ acknowledges support from the Hearne Institute for Theoretical Physics, the National Security Agency, the Army Research Office, and the Disruptive Technologies Office.