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by mmaroti 1794 days ago
I think you need more assumptions. This satisfies your requirements:

X(0) = 0000, Y(a) = 0001, X(a) = 0011, Y(2a)= 0111.

1 comments

|X(0) - X(a)| = 2, not 1 and X(a) != Y(a)

The subtler issue is that it's a counterfactual question. What would have happened if I had measured or been able to measure all three angles 0, a, 2a? In this case the bit string is the same except for the 1% difference. In other words, X(t) = Y(t), for all t.

The argument is essentially trying to construct a "hidden variable" model and showing that it can't work.