A straightforward introduction to continuous quantum measurement

By Kurt Jacobs, Daniel Steck. 2006

609 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/8ddf0c5b5af80c47922998c00ea0b8f8325d0b0b

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Citations in the corpus

Engineered dissipation for quantum information science (2022, background): “These are weak measurements 93 .”
The role of quantum measurement in stochastic thermodynamics (2016, neutral): “Such continuous measurement is described by a QSD unraveling involving a single Lindblad operator X = L1 characterized by the Wiener increment dw(t) = dw1(t) [37].”
Introduction to quantum noise, measurement, and amplification (2008, background): “The relevant theoretical framework is that of quantum conditional evolution and quantum trajectories (see e.g. Brun, 2002; Jacobs and Steck, 2006), where one tracks the state of a measured quantum system in a particular run of the experiment.”
On-chip quantum interference of a superconducting microsphere (2016, background): “The effective measurement strength representing the continuous measurement of x̃2 [45] is given by λ ≡ g2 q |α4|(2)/κ4.”
Quantum feedback: theory, experiments, and applications (2014, methodology): “it. For a single master equation there is more than one stochastic equation that will unravel it, and it can be unravelled by stochastic equations driven either by Gaussian white noise (Wiener noise) [118, 121, 122] or by a “point process” [56, 119, 123, 124]. A point process consists of intervals o”
Do We Really Understand Quantum Mechanics? (2012, background): “For introductory texts on stochastic evolutions of the state vector and continuous measurements, see for instance [494, 495].”
Entanglement in a fermion chain under continuous monitoring (2018, positive): “For a general observable (self-adjoint operator) O, the associated monitored dynamics of the quantum state is described by the following stochastic Schrödinger equation (SSE) [53–55]: d|ψt〉 =− iHdt|ψt〉+ (√ γ [O − 〈O〉t] dWt − γ 2 [O − 〈O〉t] 2 dt ) |ψt〉 , (2)”
Nonperturbative theory of weak pre-and post-selected measurements (2011, neutral): “[59–74].”
Mechanical systems in the quantum regime (2011, background): “Most measurements are, however, not single, strong measure ments, but weak continuous measurements instead [205].”
Quantum control theory and applications: A survey (2009, neutral): “In continuous measurements, one can continuously monitor an observable of a quantum system and the evolution of the sys-tem described in terms of the measurement record can be obtained from a stochastic master equation [89].”