A straightforward introduction to continuous quantum measurement

2006/09/01 by Kurt Jacobs, Daniel A. Steck · 1 voice · 10 citations
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum optics and atomic interactions #quant-ph

paper · pdf · doi:10.1080/00107510601101934

published as Contemporary Physics 47, 279 (2006) · 24 pages, 3 eps figues. To appear in Contemporary Physics

openalex publication_date 2006/09/01 · arxiv created 2006/11/06 · arxiv published 2006/11/06 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04

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.

Citations

• Dynamics of a mesoscopic charge quantum bit under continuous quantum measurement
• Continuous quantum measurement and the quantum to classical transition
• High-fidelity measurement and quantum feedback control in circuit QED
• Information Tradeoff Relations for Finite-Strength Quantum Measurements
• Adaptive quantum measurements of a continuously varying phase
• Robust quantum parameter estimation: Coherent magnetometry with feedback
• Feedback-control of quantum systems using continuous state-estimation
• Emergence of Chaos in Quantum Systems Far from the Classical Limit
• Linear quantum trajectories: Applications to continuous projection measurements
• Transition to classical chaos in a coupled quantum system through continuous measurement
• Quantum Feedback Control of Atomic Motion in an Optical Cavity

Cited by

• Dynamics of colored-noise-driven stochastic Schrödinger equations
• Deterministic Equations for Feedback Control of Open Quantum Systems
• A unified picture for quantum Zeno and anti-Zeno effects -- a review
• Inequality for von Neumann entropy change under measurement and dissipation
• Time-averaged continuous quantum measurement
• Quantum thermodynamics of continuous feedback control
• Entanglement generation and dynamical equilibrium within de Broglie Bohm theory
• Quantum information engines: Bounds on performance metrics by measurement time
• On a time-resolved interpretation of the Husimi function
• Feedback Control in Quantum Optics: An Overview of Experimental Breakthroughs and Areas of Application

Discussions

• A quantum system monitored by a sequence of weak measurements obeys a stochastic equation of the form (taken from Eq.(30) of Ref. [1]): $$ \textrm{d}|\psi_t\rangle = \{ -(i/\hbar) H \textrm{d}t -k(X-\ [stackexchange, 3 points]