Small Transmitting Loops (STL) are loops of less than about 0.1λ in diameter or about 0.3λ in circumference. Below these limits, the current around the loop is almost uniform and this permits a simplified analysis. (A stricter definition of 0.3λ in circumference could be argued.)
These antennas are ascribed all sorts of magic properties, low noise, able to create band openings when conditions are poor etc.
The efficiency of an STL depends on radiation resistance Rr and loss resistance Rloss. Efficiency η=Rr/(Rr+Rloss).
Radiation resistance of an STL is approximately proportional to the fourth power of frequency.
In a well implemented STL, almost all of the loss is conductor loss which is approximately proportional to the square root of frequency by virtue of skin effect.
Above is a plot of efficiency vs normalised frequency for a loop where conductor loss dominates. It can be seen that at a frequency of half that where the efficiency is 50%, efficiency is just 8%, and half that again is 0.8%.
Performance typically drops quite quickly for loops less than λ/20 diameter at the operating frequency.
If you implemented a 1m diameter loop with 13mm diameter copper tube and a near lossless tuning capacitor and feed system on 14MHz, you should achieve an efficiency of about 50% or 3dB less than an ideal loop at great height above ground. That same loop on 40m would have an efficiency of around 8% or 11dB less than an ideal loop, and on 80m, efficiency of 0.8% or 21dB less than an ideal loop.
The VSWR=2.6 bandwidth of such a loop is just over 3kHz on 40m, not really adequate for SSB telephony and on 80m, VSWR=2.6 bandwidth is just over 2kHz, suitable only for CW or narrow band digital modes.
The most likely explanation for observations that these are low noise antennas is that they are inefficient, they have low gain.
Now you can improve on the configuration mentioned. You could increase the conductor size (conductor losses are approximately proportional to diameter), but the greatest improvement is from increasing the loop diameter. It is easier to do a lot worse with poor loop conductors (coax braid, small diameter wires), improvised lossy capacitors such as PCB, broadcast variable capacitors, coax line sections etc, though such loss had the benefit of increased bandwidth.
There are lots of articles on the magic of these things, but few have credible objective measurements that support the claims.
There is no magic.
Like all physically small antennas, they trade bandwidth for size, and efficiency is very sensitive to design and construction. You can trade bandwidth for even lower efficiency, and it seems that is commonly done.