Leinster haven't lost in Europe for close to 16 months and only recently relinquished an unbeaten run in all competitions that dated back to mid-September.
The Blues will understandably be heavy under dogs for their last eight encounter - especially as they have registered just one win in their last 10 meetings with the Irish province - but Baber insists it's exactly the kind of challenge every professional rugby player should look forward to.
"It doesn't get better than this," Baber, who is convinced his troops can cause an upset if they focus on performing to the best of their own ability, told this website.
"That's where you want to be as a professional and the group of boys that we've got are quite capable of going out there and putting in a performance that can give us progression to the semi-final.
"They're the European Champions for a reason, though. They're very comfortable in several different aspects of their game, not least the contact area. I could go and on in terms of their kicking game, the setpiece etc but we've got to get what we've got to get right, right.
"We don't want to concentrate on what the opposition are doing. We'll obviously look at how we can negate their threats but it's also about creating our own opportunities.
"We've got the game, and the personnel as well, that can upset the way they play, their shape and their rhythm, and then we've got to be sharp enough to capitalise on the two or three opportunities that we do get."
Despite coming within just a few minutes of earning a home tie in the knockout stages and avoiding facing the defending champions in their own backyard, Baber has given no thoughts as to what might have been had Edinburgh not picked up a last-gasp bonus-point try against London Irish to deny his team top spot in Pool 2.
Instead, Baber and fellow Blues coach Justin Burnell have been focusing on the positives of an impressive Heineken Cup campaign that saw them register five wins in six attempts.
The Blues set out to make it to the quarter-finals in Baber and Burnell's first season in charge and they've done just that thanks to double successes against Irish and Racing Metro and a home win over Edinburgh in Round 3.
"It was crucial for us to progress in Europe this season," added Baber.
"We did exactly what we'd set out to do, so that was an achievement.
"We played well in two or three games in the pool but we let ourselves down in Edinburgh when we were in with a shout of winning that game. We came away with a bonus point there, though, and everywhere we've gone we've picked up points and that's being crucial in making it through.
"Now it becomes all about progression beyond the quarter-finals. We'll have a good focus on turning over the champions in their own backyard."