Straightforward length measurement (by interferometry) has a resolution limited by the wavelength of light that can be generated with lasers, so up to the near ultraviolet, at a few hundred nanometers.
Resolution smaller than a wavelength can be achieved with vernier techniques (like in a caliper), but those require a pair of light sources with precise frequency/phase relationships between themselves, which are difficult to make at such high frequencies, so it is hard to improve much the resolution.
I have not looked to see if there have been any progresses in recent years, but I would guess that a very approximate limit for the resolution of length measurement would be around 100 nm. So measuring the length of an 1 meter stick might provide up to log_2(10^7) bits, so about 23 ... 24 bits.
Of course, any temperature fluctuation would change the length of the stick by much more than the resolution.
However that can be avoided by encoding the information not in the absolute length, but in the ratio between the lengths of 2 segments marked on the stick.
No matter what, it is possible to write much more bit symbols on any stick than it is possible to encode in the measurements of one or a few lengths marked on the stick.
That is due to the fact that halving the size of a bit symbol doubles the quantity of information written on the stick, while halving the length corresponding to the measurement resolution provides just 1 single bit of extra stored information.