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Using the space-time analogy, we compare the performance of quantum temporalimaging with its classical counterpart. We consider a temporal imaging scheme,based on the sum-frequency generation (SFG) time lens, but our results can beapplied to other temporal imaging schemes such as, for instance, four-wavemixing. Extending the theory presented in our previous publications, in thispaper we take into account the finite time aperture of the imaging system,characterized by its pupil function. Using the quantum theory, we obtain aunitary transformation of the quantum field from the input to the output of theimaging scheme and identify the contribution of the vacuum fluctuations missingin the classical theory. This contribution plays a key role in the quantumtemporal imaging of nonclassical temporal waveforms, characterized bynonclassical fluctuations of the electromagnetic field. As an example, weconsider quantum temporal imaging of broadband squeezed light and formulate thecriteria for conservation of its squeezing properties at the output of thesystem.

Space-time duality and quantum temporal imaging