What is the function of variable inlet guide vanes in terms of pressure change?
You need to be careful in understanding the significance of the variable guide vanes (VGVs) being variable.  You could think of them as a bit like venetian blinds -  when they they are most open they present the least obstruction to the air flow, much as you get the most light through a set of blinds when they are at the right angle to the incoming light. As you close them, you get less flow (light) through them, as they present a greater obstruction to the flow.

The VGVs are only variable to maintain stable flow in the compressor at conditions away from the design condition.  The design condition for jet engines is always high power during cruise (or at the top of the initial climb to be pedantic), so the VGVs only start to close at reduced powers.

At high power the vanes are at their most open to maximise flow through the engine, minimising pressure losses across them and maximising thrust.   As they are gradually closed when power is reduced, they present more of an obstruction to the flow (acting as effectively a variable area throttle valve in the path of the flow being closed down), so presenting an increased pressure ratio loss (or if you prefer reduced pressure recovery).  

The increased use of VGVs really shows designers pushing at the limits of airflow stability in pursuit of better efficiency by maximising pressure ratio per stage at the design condition, at the cost of the increased weight of the mechanisms to drive the VGVs.

Not sure I expressed that very well, but first post on stack exchange.