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Summary form only given.Two-photon entangled states generated by the nonlinear optical process of spontaneous parametric downconversion (SPDC) have found extensive use for testing the basic foundations of quantum theory. At the same time, the area of ultrafast femtosecond optics using conventional lasers has blossomed. We have carried out a set of experimental and theoretical studies at the crossroads of these two fields. The pulsed light is generated by a tunable Ti:sapphire femtosecond laser. After conversion to second harmonic, the pulses are directed towards the downconversion nonlinear crystal. A two-photon quantum state is generated by means of type-II SPDC in a collinear configuration. We have experimentally demonstrated that the quantum interference of a twin pair generated in the nonlinear crystal degrades significantly as the duration of the femtosecond pump pulse becomes shorter than the coherence time of the signal and idler photons. In this domain the spectrum of the pump pulse is wider than the spectral widths of the signal and the idler photons, which are defined by the natural phase matching in nonlinear parametric processes. The pulsed pump introduces a knowledge in principle of the creation time of the photon pair. This additional information destroys the quantum interference. We have developed a different (noninvasive in terms of total number of photons) approach to restoring the quantum interference of entangled photons with femtosecond pulses, based on the indistinguishability of quantum amplitudes that lead to a final event. We compare and contrast these approaches. We discuss implications of our results in the areas of multiple-particle quantum interferometry and practical two-photon cryptography.