Non-demolition measurements of observables with general spectra

Thursday, 29 June, 2017

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


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