In principle it is possible to use a simple RC delay and send its output to an XOR gate. The other input of the XOR will be connected to the non-delayed signal. Roughly RC≈pulse width (to be more precise you have to know the threshold of the gate).
In general rise and fall thresholds will be different one each other, so if you need a pulse on both positive and negative edge, having the same timing you'll have to add diodes in order to charge and discharge the capacitance on two different resistors.
However I expect this circuit not to be very accurate and 2ns resolution seems to me hard to reach. Furthermore the jitter introduced could be even higher than 2ns