Quantum Memory Effects in the Measurement of Observables with a Continuous Spectrum
In the measurement of a continuous observable Q, the pure components of the reduced state do, in general, depend on the initial state. For measurements which attempt to localize the measured system in a certain region R, the localized wave functions are proportional to the original wave function outside of R. This `quantum memory' effect shows that it is not possible to perfectly localize a quantum particle.
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