How to measure correlation between 1 bit samples and theoretical original waveform?
I've sampled it at a 1 bit resolution (as 8 bit oscilloscope readings &amp; 0b1)

No. Taking the LSB is NOT 1 bit quantization. A one bit quantizers are not trivial to design. For a zero mean signal that's reasonably symmetrically distributed over positive and negative values, you can just take the sign bit. For signals that are asymmetrically distributed around their mean, designing a decent 1 bit quantizer takes a bit of work.
In your example you should quantize so that you get a &quot;1&quot; of the signal is above the mean and and &quot;0&quot; if it's below the mean. If you do this, you will see that both quantization noise and quantized signal are highly correlated with the original signal. Both will be periodic with the same period.
If you want to study quantization noise, I recommend starting with higher bit levels, i.e. where the amplitude of the signal is much larger than the quantization steps. This makes the choice of quantizer very simple and in most case you can assume that the quantization noise is uniformly distributed. Otherwise, you need to tackle the subject of &quot;optimum quantizer&quot; which requires some non-trivial math.