I prefer
This is the best performance I have ever seen.
over
This is the best performance I ever saw.
They mean the same thing (namely, that the person saying it witnessed the best performance thus far in their life) unless context implies otherwise.
This is the best performance I will ever see.
The sentence means they will never see a better performance; it's impossible for another performance taking place in the future to be better than this one.
While it might make syntactical or logical sense to answer the question with "Yes," that's simply not how anybody ever does reply to it.
Illogically, "No" is the normal response to both:
Have you seen this movie?
Haven't you seen this movie?
This is one of those cases (there are actually many of them) where the English language takes a detour from common sense and falls back on actual usage.
Another way of answering the question, which actually makes sense, is simply:
I haven't.
If you don't want to say something that seems off, you can reply in that fashion. It may sound be a bit more formal, but it's still quite acceptable.
Other possible answers, which also make sense but are much less common and sound slightly awkward, include:
That's correct, I haven't.
That's right, I haven't.
Normally, those would be given in response to a statement (you haven't seen this movie) rather than a question.
Best Answer
They are both correct, and there is no difference in meaning.
I believe there was a very pedantic belief in the past the parts of the verb should be kept together (I happened to see an example in another question moments ago). This was related to the idea that led to the belief split infinitives were wrong. You can see a discussion here.
So just as past grammarians would have said one should not say 'to probably see', they would also have said to avoid 'have probably seen'. It was fake grammar, and has long been discarded.
The example I just saw in another question was 'one could never tell'. This is a common phrase, but is much more common as 'one never could tell' or 'you never can tell'.
Even the people who still bemoan split infinitives will usually not know or care about the more 'advanced' version of the 'don't split the parts of verbs' rule.