Non-demolition measurements of observables with general spectra
Miguel Ballesteros, Nick Crawford, Martin Fraas, Jürg Martin Fröhlich, Baptiste Schubnel · Contemporary mathematics - American Mathematical Society · 2018
It has recently been established that, in a non-demolition measurement of an observable N \mathcal {N} with a finite point spectrum, the density matrix of the system approaches an eigenstate of N \mathcal {N} , i.e., it “purifies” over the spectrum of N \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 N \mathcal {N} . Our methods highlight the connection between the theory of non-demolition measurements and classical estimation theory.