"So, when you apply a measurement operator on the state of particle a, you know something about particle b in the entangled case."
You do now know something about particle b, but your explanation suggests that information existed all along.
You do now know something about particle b, but your explanation suggests that information existed all along.
This is why I object to classical analogies using envelopes and cards and pennies that end with "Yeah QM is strange". It's really a fundamental physical/mathematical effect, and it's much less intuitive if you make a mapping to objects in a classical world. I often feel conceptual maps to information worlds (like books and the internet) are more intuitive.