My idea is that it takes two wires from each cable (i.e. left positive and left negative) to transport the left signal from i.e. a CD-player. If these two have the opposite signal, you can use a sort of technic that normally are being used in balanced systems.
That's where the confusion lies: Your separate left and right phono cables are NOT differential pairs. They are single-ended.
Let's start with the signals themselves. Each of your two phono cables has a single center conductor and a shield. The shield is most likely tied to ground, and the center conductor is carrying the signal. If you have a multimeter, check continuity between the shields on the left and right cables... I bet they're both grounded, and thus nearly a dead short. These are single-ended signals, measured relative to ground (the shield in both cables).
An XLR connector - or indeed, any truly differential signal - has TWO signal conductors in addition to a ground reference. The signal of interest is measured ACROSS those two conductors. In a purely differential environment, those two conductors are all that you need; you don't need a ground reference at all, because the signals on those two conductors are not relative to ground, they are only relative to each other. (In the real world, you probably [but not definitely!] can measure one of them relative to ground but that misses the whole point of differential pairs, as we'll see below.)
As noted by another respondent herein, the two wires in a proper differential pair have identical but inverted signals. Imagine the original signal is a 2Vpp sine wave. When the sine wave is at its positive peak (+1V), a scope viewing both wires of the differential pair would show one wire at +0.5V and the other at -0.5V. The voltage difference between them is thus +1V. At the negative peak, the first wire would now be at -0.5V and the second would be at +0.5V, and the voltage difference between them is -1V. The
differential between them is swinging a full 2Vpp, but viewed
individually each wire only sees 1Vpp.
Why would we do this? Two reasons: Isolation and noise immunity.
Isolation is a secondary benefit and results from the fact that, with a purely differential pair, you don't need to connect the grounds of the equipment on either end of the wire. This is especially critical in some audio (and video) environments. The two pieces of equipment could be on different AC power phases, for example, leading to hum problems. The two grounds on either end can be at different voltage potentials (ground is NOT always ground, no matter what they told you in school!) which would cause current to flow in the cable shields, another source of hum and interference. By isolating the grounds, the only electrical connection between the pieces of equipment can be the differential pair itself.
Noise immunity is a primary benefit of differential signals. It works because the two wires in the differential pair have signals that are identical except for being exactly 180 degrees out of phase ("inverted" is probably the better, more general term here). The signal of interest is thus the mathematical difference between the wires. Now, imagine that along the way, your differential pair picks up some noise. Let's say it's a 60Hz sine wave from some mysterious, unknown source
. Since the differential pair is traveling together - in fact, in the case of XLR microphone cables, the differential pair is actually twisted together - to encourage them to both pick up
exactly the same noise. Thus in this example they both now have a nasty 60Hz sine wave. But crucially, that sine wave is the
same on both wires.
On a scope, to the naked eye, your signal now looks totally trashed... but what's really happening is that your original signal is differential, while the 60Hz is common to both wires (aka "common mode"). If you have an identical sine wave on two wires and measure across them, what is the voltage? Zero! Because the voltage on the two wires is always the same, you'd measure zero differential across them. (Importantly, think about what would happen if you measured just one wire relative to ground... you'd see a sine wave, right? But measured across the differential pair you'd see nothing at all, because they're always the same voltage.)
All of this is wondeful, but how do you use it? Well, a transformer is inherently a differentiator. Hook your differential pair across a transformer winding and you get zero for common mode signals but anything differential generates an associated magnetic field in the core. An opamp configured as a differential amplifier does the same thing: Common mode signals are rejected (because there is no voltage difference to be amplified) while differential signals are recovered. Voila - now your 60Hz is gone.
With all of this background: You cannot treat single ended signals as differential signals. They are not the same. Might it work? Sure... a diffamp will usually work with one input grounded, which is what your single ended source would do. But you're not getting all of the advantages that people expect from truly differential signals, and you're working really hard to not get them.
Likewise, you cannot simply take the center conductors of the left and right channels and run them into a diffamp. As another respondent noted, at best you'll create a low-quality karaoke machine by removing centered signals (such as the vocals) and the result will sound really weird.
The left and right channels are NOT a differential pair and cannot be processed as such. You cannot expect noise reduction with differential processing of single ended signals.
If the above was redundant and you already knew all of it, my apologies. Otherwise, hope it helps!