General quantum constraints on detector noise in continuous linear measurements

Haixing Miao
Phys. Rev. A 95, 012103 – Published 5 January 2017

Abstract

In quantum sensing and metrology, an important class of measurement is the continuous linear measurement, in which the detector is coupled to the system of interest linearly and continuously in time. One key aspect involved is the quantum noise of the detector, arising from quantum fluctuations in the detector input and output. It determines how fast we acquire information about the system and also influences the system evolution in terms of measurement backaction. We therefore often categorize it as the so-called imprecision noise and quantum backaction noise. There is a general Heisenberg-like uncertainty relation that constrains the magnitude of and the correlation between these two types of quantum noise. The main result of this paper is to show that, when the detector becomes ideal, i.e., at the quantum limit with minimum uncertainty, not only does the uncertainty relation takes the equal sign as expected, but also there are two new equalities. This general result is illustrated by using the typical cavity QED setup with the system being either a qubit or a mechanical oscillator. Particularly, the dispersive readout of a qubit state, and the measurement of mechanical motional sideband asymmetry are considered.

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  • Received 19 May 2016
  • Revised 24 August 2016

DOI:https://doi.org/10.1103/PhysRevA.95.012103

©2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
General Physics

Authors & Affiliations

Haixing Miao

  • School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom

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Issue

Vol. 95, Iss. 1 — January 2017

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