What's The Difference Between Learning Values And Learning Relationships?
Relationships carry information that single facts do not, and they are inherently harder to extract
You can carefully examine a system and still overlook the essentials.
You look at one output. You learn one fact.
You look at another output. You learn another fact.
And yet the question that interests you may remain unanswered. There is obviously a gap. If you don’t clearly recognize this, nothing about quantum advantage will make sense later on.
So let’s be clear about this.
A local observation tells you a value. In contrast, a global property tells you how values relate to each other. These are not the same types of knowledge. A value exists in one place. A relationship exists across multiple places.
You can’t reduce one to the other through cleverness.
Why can’t I do that?
If a global property depends on local values, it should be sufficient to learn those values, no? If you know all the parts, how could you possibly miss the whole? So why not just try a few results and deduce the rest from them?
This instinct is reasonable. However, it fails for a specific reason that has nothing to do with quantum mechanics.