Filtering a QPSK signal
I think a picture of the QPSK constellation would be helpful to intuitively see what is occuring. Consider two possible transitions in the QPSK constellation as shown below, from &quot;B&quot; to &quot;C&quot; (180° transition) and from &quot;A&quot; to &quot;C&quot; (90° transition):

Note the difference between a 180° transition as when we move from &quot;B&quot; to &quot;C&quot; compared to a 90° transition in moving from &quot;A&quot; to &quot;C&quot;. The instantaneous amplitude will be the vector magnitude at any point along the dashed lines during the transition. If the signal and has infinite bandwidth (not realistic, but if), the transition will be instant and therefore the vector magnitude will never change (will be constant envelope). However with any filtering there will be a finite time to complete the transition, and we will observe the magnitude change according to the vector length along the path taken. I placed stars where the magnitude is minimum in each case, and it is clear how in the 180° case where we pass through the origin, the magnitude approaches zero while in the 90° case the reduction in magnitude is much less.
Based on actual filtering and prior symbol history the paths will deviate somewhat from what I shown in the picture above, but the concept still holds. For example below shows a constellation of a root raised cosine signal where we can make out the same effect with the different transitions.

Minimizing the peak to average ratio is important in power sensitive applications such as Satcom and battery operated devices. This is the motivation for modified waveforms such that no trajectories go through the origin such as $\pi/4$-QPSK and waveforms that are constant envelope such as MSK and and FQPSK.