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arXiv · 1706.09584

Non-demolition measurements of observables with general spectra

M. Ballesteros·N. Crawford·M. Fraas·J. Fröhlich·B. Schubnel
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Abstract

It has recently been established that, in a non-demolition measurement of an observable $\mathcal{N}$ with a finite point spectrum, the density matrix of the system approaches an eigenstate of $\mathcal{N}$, i.e., it "purifies" over the spectrum of $\mathcal{N}$. 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 $\mathcal{N}$. Our methods highlight the connection between the theory of non-demolition measurements and classical estimation theory.

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M. Ballesteros, N. Crawford, M. Fraas, J. Fröhlich, B. Schubnel. 2017-06-29. Non-demolition measurements of observables with general spectra. https://arxiv.org/abs/1706.09584

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