Any air compressor termed as the quietest air compressor is not 100% quiet. They can still produce noises but the range of those noises are so less that they can be easily tolerated. You can even whisper to your colleagues and talk without shouting.
As per researchers, any air compressor that has a sound production up to 80DB is considered quiet. As per my research, I have given a list of products that gives you a variety of air compressors having noise production between 60 DB to 75 DB.
Secondly, oil-lubricated motors of air compressors will further suppress the noise, resulting in an ultra-quiet environment of your workplace. However, this can be at the expense of high maintenance.
If you are looking for a quiet portable air compressor, then you should invest in an isolated rubber chamber that can minimize the sound production. Nearly all portable air compressors have this rubber chamber nowadays.
People with a strong budget can select ultra-advanced tools with mufflers around them. These tools are rated as the ultra-quiet soundproof category.