@Grooved has the right idea with
DeltaWave. It's fairly easy to measure differences between two music tracks as long as they are not too different (use the same masters, for example). By the way, DW can also be used to determine if two tracks come from the same master.
Since I don't have access to an MQA-decoded track to match against an equivalent PCM file, I'll start with an example from 2L
website, comparing the un-decoded MQA file to the PCM one. This is for track 38, Mozart's Violin concerto in D major, first 2 minutes analyzed:
Un-decoded MQA (24 bits, 98MB size) vs. PCM (16 bits, 48MB size), 44.1kHz, track 38
This is showing the un-decoded MQA file compared to PCM. This would be the case of someone playing the MQA-encoded content on a non-MQA-capable DAC.
Spectra of the two files (blue is the PCM, white is MQA-encoded):
The differences between two spectra, becomes significant above 20kHz, but pretty noisy since there's not a lot of signal there:
As you can see, the RMS Null is -71dBFS. That's not a bad result for an analog/digital loopback recording, but remember that this comparing two pure digital files.
Spectrum of the error signal (null/delta file) goes a bit above -100dBFS, but only above 18kHz:
Difference in phase gets noisy with higher frequencies, but remember that the signal level falls below -96dBFS at around 16KHz, so noise starts to creep in:
PK Metric, for completeness, shows nothing in the difference signal that should be audible based on various perception-based weights (ERB smoothing, 400ms averaging, and equal loudness curves applied):
Impulse response as derived from these two files:
From DeltaWave log, 50% of samples in the two files will match perfectly at 11.6bits. In other words, signal and noise carried in both files will match with mathematical precision (losslessly) at around 11 bits out of 16. Whatever MQA encoding is doing to the file, it's altering around 5 of the least significant bits.