Quadraphonic records (LPs to you and me)

I am looking at Ebay uk an item called
CARLY SIMON ~ HOTCAKES ~ USA QUADRAPHONIC STEREO AUDIOPHILE LP
So the "stereo" word is out of place, or indeed wrong?

The Bryston very successfully codes 2 channel into 7.1.
I never play analogue into stereo 
So the quadraphonic lps need a special cartridge ... and phonostage then. So presumably playing with a normal cartridge and phonostage some channels are missing, hence maybe a weaker sound for a number of reasons, presumably, from what you are saying?
Must be for a very limited market place these records then

So is any quad beneficial element picked up in a normal cartridge and phonostage, or just "wasted"?
From what you are saying all elements are in principle "recovered"?
I feel I am either being stupid or missing something here
If the Bryston decodes elements into separate aspects to surround speakers I was wondering if the input already into 4 may provide an easier or more varied decoding

Ok but  a proper decoder is what ...?

So you might recommend playing  a quad stereo lp on a normal set up?
Whereas someone else said it would be less due to lost components

Why do you need 7.1 if you’re playin’ stereo vinyl at home ?

I do not have at the moment a separate 2 x  mono preamp (one however is being built for me bespoke by Tom  Evans)
So the phono goes into my sp3 where it is decoded into 7.1 - which separates the signals into excellent splits around surround speakers. It does not just "surround" the sound but splits them up in a good way. E.g in Mandolin Wind there are 3 guitars that in stereo sound like one or maybe two (dependent on the speakers!). The Bryston splits those into different speakers so you can hear quite distinctly. Often also percussion is separated to hear the decay of those items well as they are often coming out of a surround and not L or R. Great for me as I used to play in an orchestra and I love being "in" the sound rather than face a wall of it.
Not many companies' products do this. Bryston and Lexicon do very well and Chord did some time back