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arXiv:1906.07403 · Automatica

Exponential stabilization of quantum systems under continuous non-demolition measurements

Gerardo Cardona, Alain Sarlette, Pierre Rouchon

Published Nov 28, 2019• 42 citations
arXivHTMLPDF
DOI
10.1016/j.automatica.2019.108719

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It has recently been established that, in a non-demolition measurement of an observable N\mathcal{N}N with a finite point spectrum, the density matrix of the system approaches an eigenstate of N\mathcal{N}N, i.e., it "purifies" over the spectrum of N\mathcal{N}N. We extend this result to observables with general spectra. It is shown that the spectral density of the state of the system converges to a delta function exponentially fast, in an appropriate sense. Furthermore, for observables with absolutely continuous spectra, we show that the spectral density approaches a Gaussian distribution over the spectrum of N\mathcal{N}N. Our methods highlight the connection between the theory of non-demolition measurements and classical estimation theory.