Using CD player without Preamp?

Maybe you could explain how data is lost. It doesn't have to be so.

It is lost through "quantization" error due to rounding. Normally a CD will be dithered when it is produced from a higher resolution source - preserving 93 db SPL of dynamic range. Not ALL digital volume controls are implemented properly and include the necssary dithering. I think that was what Kal's warning is about.

If you turn the volume down to low levels you may be left with only 5 bits with loads of horrible harmonic distortion - if this is simply truncated or re-sampled rather than re-dithered before re-sampling then it can sound awful....many PC software volume controls do this and sound awful - PC audioo can be a minefield.

The gain of the analog output circuitry can be changed
under digital control.

Exactly! A Crystal digitally controlled resistor network volume control chip with
0.5 db SPL intervals costs around $10 and has excellent performance.
(Surprisingly this is actually an expensive item as far as electronics go...although
it is far cheaper than the front fascia of most amplifiers or the volume control
knob itsef!!!!)