The Beckenstein Bound Is the Number of Basis States, Not the Quantum State

In a single spin is described by a two dimensional space of possibilities called the block sphere. A sphere just like a real number has an infinite number of points. So it's not a real numbers worth of information that is required to tell you what quantum states form the basis for the system we're looking at. But we never have that information. We don't have access to it. We all of our measurements only have a finite resolution. Right?