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arXiv:1202.4065

Quantum limit in continuous quantum measurement

Cheng-gang Shao

Published Feb 18, 2012• 0 citations
arXivHTMLPDF

Abstract

An inequality about quantum noise is presented with the imprecise measurement theory, which is used to analyse the quantum limit in continuous quantum measurement. Different from the linear-response approach based on the quantum relation between noise and susceptibilities of the detector, we provide an explicit functional relation between quantum noise and reduction operator, and show a rigorous result: The minimum noise added by the detector in quantum measurement is precisely equal to the zero-point noise. This conclusion generalizes the standard Haus-Caves quantum limit for a linear amplifier. We also discuss the statistic characters of the back-action force in quantum measurement and show on how to reach the quantum limit.

DOI
10.48550/arxiv.1202.4065

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Abstract This chapter covers the basics of quantum noise and the subtle aspects of Caves’ theorem on quantum-limited amplifiers. It introduces on the one hand the susceptibilities of a quantum measurement system, and on the other the crucial Nyquist model of dissipation, which is essential to the understanding of the quantum fluctuation-dissipation theorem for a passive system and the constraints on noise for an active system. Great insight on the paradoxical properties of quantum noise can be obtained by comparing, in the calculation of the noise of an active circuit, the point of view of susceptibilities and response functions with the point of view of input-output theory dominated by the formalism of the scattering matrix. In particular, the chapter provides an explanation of the existence of different optimum working points for a nonmatched amplifier if one optimizes the gain or the noise.
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