Question: "What are the things that are necessary for this process to function?"  Context: "The development of quadraphonic records was announced in 1971. These recorded four separate sound signals. This was achieved on the two stereo channels by electronic matrixing, where the additional channels were combined into the main signal. When the records were played, phase-detection circuits in the amplifiers were able to decode the signals into four separate channels. There were two main systems of matrixed quadraphonic records produced, confusingly named SQ (by CBS) and QS (by Sansui). They proved commercially unsuccessful, but were an important precursor to later surround-sound systems, as seen in SACD and home cinema today."  Answer:
phase-detection circuits in the amplifiers