Let's extend the thought experiment a bit. Suppose technology is developed to separate the twins. They rely on their shared brain parts for vital functions, so where we cut nerve connections we replace them with a radio transceiver and electrode array in each twin.

Now they are communicating thoughts via a prosthesis. Is that not communication?

Maybe you already know what it is like to be a hive mind with a shared consciousness, because you are one: cutting the corpus callosum creates a split-brained patient that seems to have two different personalities that don't always agree with each other. Maybe there are some connections left, but the bandwidth has been drastically reduced. And even within hemispheres, the brain seems to be composed of yet smaller modules. Your mind is made of parts that communicate with each other and share experience, and some of it is conscious.

I think the line dividing individual persons is a soft one. A sufficiently high-bandwidth communication interface can blur that boundary, even to the point of fusing consciousness like brain hemispheres. Shared consciousness means shared qualia, even if that connection is later severed, you might still remember what it was like to be the other person. And in that way, qualia could hypothetically be communicated between individuals, or even species.