As humans, our eyes contain 3 different types of cones (red, blue, and green). With these we can see around 1 million different colors.

But Mantis Shrimp have 16 different types of cones in their eyes! And with those 16 cones they can see a whopping... 16 colors.

While our brains allow us to mix and match the different bands of light our eyes detect in order to "see" a wide variety of colors, Mantis Shrimp lack that ability. What they detect is what they get, there's no neural post processing, or at least not any that allow the perception of mixed colors.

I'm not sure what you mean by "advanced" but they're really not

An Immense World by Ed Yong had a section on Mantis Shrimp and while their fascinating creatures with a really interesting vision system, their color perception isn't all it's cracked up to be

I'm reciting this from memory so if anyone knows better please correct me:

Mantis Shrimp have compound eyes with three sections: 1) the main section detects movement and is what they primarily use to see 2) the second section detects color. When the shrimp detects movement it will look at whatever it was with it's color detecting section to determine if it's prey or predator. This is a whole separate section of the eye and is unlike how ours function. The reason why the shrimp has so many detectors is because, unlike our eyes, the shrimps eyes don't combine different color receptors to see color. The book likened it to a bar code scanner that uses the presence of certain color combinations to detect what's there 3) one really neat thing the mantis Shrimp can do is see spiralized polarized light. We cannot see polarized light but there's a lot of b polarized light under the ocean so seeing it is fairly common. What's NOT common is polarized light that travels as a spiral. Mantis Shrimp seem to have evolved the ability to create spiralized polarized light and use it to communicate. As far as we know no other animal can make or see it.

Squid have better arranged eyes then us but I don't know much about Mantis Shrimp eyes.