Follow up question regarding: "Complex sampling can break Nyquist?"
To represent a complex baseband signal in the range $[-B/2,B/2]$ you need either $2B$ real samples or $B$ complex samples per second.

To take real samples, you write the signal as $I(t)+jQ(t)$, with $I(t)$ and $Q(t)$ real, and sample each one at $B$ real samples per second, for a total of $2B$ real samples per second. It should be clear that you can't downsample without aliasing.

You can also take complex samples at $B$ samples per second (which is just a different way of thinking about the real sampling described above). This allows you to represent the entire band $[-B/2,B/2]$. Downsampling in any way will also result in aliasing.

To be more specific regarding your application: You have a bandpass signal with bandwidth $B$ and take real samples at rate $2B$. When you calculate the complex envelope, the I and Q components can be sampled at a rate of $B$ real samples per second each. The complex envelope can also be sampled at a rate of $B$ complex samples per second. In any case, you end up with a total of $2B$ real samples per second.