No film has ever had a cinema release with a quadraphonic sound mix as such mixes lack the all-important screen centre channel. The nearest approximation was the "Quintaphonic" sound system used for the initial 1975 release of "Tommy"; this used the combination of a quadraphonic system (Sansui QS matrix) with a discrete centre channel. However this system relied on expensive magnetic-sound film prints and was never used again. "Quadrophenia" used the Dolby Stereo system which by 1979 was well on its way to becoming the de-facto standard sound system for 35mm film prints. Dolby Stereo uses a 4-channel (left, centre, right & surround) mix which is fed through the Dolby Stereo (aka Dolby pro-logic) matrix so that it can be recorded on two optical soundtracks on the print. In the cinema a Dolby Stereo decoder recovers the 4 channels. The early DVDs of "Quadrophenia" used this soundtrack so anyone who fed it through a pro-logic decoder would have heard the original cinema mix.
From the mid 1990s onwards almost all film prints intended for cinema release have also carried a digital 5.1 sound mix in either Dolby Digital, DTS or SDDS or, most commonly, all three. In addition they also carry an analogue Dolby SR stereo soundtrack as a back up. Any 21st century re-release of "Quadrophenia" would have either used the original Dolby Stereo mix, a 5.1 digital one, or both.