Mike Okuda, one of Star Trek's technical directors, the originator of the Okudagram, and the co-author of several Star Trek books, including the Star Trek: The Next Generation Technical Manual and the world-famous Star Trek Encyclopedia, answered the telephone to find someone on the other end asking "How does the Heisenberg compensator work?" to which he answered "Very well, thank you," and put the phone down, because the Heisenberg compensator is a device used in the transporter system to compensate for the Heisenberg Uncertainty Principle (that you cannot know a particle's position and velocity at the same time) which would otherwise render transporters theoretically impossible (as an afterthought, Zulu One refers the reader to amazingly long sentences).

Actually, you don't need any kind of Heisenberg compensator in order to teleport particles. (and, with sufficiently advanced technology, complex systems like human beings) You need a pair of particles in a state of quantum entanglement for every particle that you send, one at the source and one at the destination. (Entangled particles will always be in the same state, if completely isolated from the environment, even if separated by large distances, except that you can't really tell, because a classical measurement will break the entanglement) The sender then uses a special quantum gate to perform a joint measurement on the particle that they want to send (the "source" particle) and their side of the entangled pair. This measurement will change the state of the source particle, as well as the state of the entangled one. (actually, the state of both entangled particles, including the one on the receiver's side, because they are entangled) The sender then transmits the measurement results to the receiver using a classical channel. The receiver performs a reverse operation on their side of the entangled pair, using the information received from the sender. This will have the effect of changing the state of the (formerly) entangled particle into the initial state of the "source" particle, effectively reproducing the initial particle on the receiver's side.

Sounds like magic? Well, it is very advanced technology...

(The deep technical details, ie. the good stuff omitted. This is little more than theoretical physics right now, but these scientists always surprise us...)

In Star Trek technobabble, Heisenberg Compensators are actually a sort of inside joke for real geeky scientists who watch the show. According to Werner Heisenberg's Heisenberg Uncertainty Principle, the idea of making transporters work is theoretically impossible. You can't know the exact location of an atomic particle without losing track of where it's going, or how fast. And when you try to figure out how fast it's going, you lose track of where it went, or where it is. So taking apart a human being and then putting him together on the planet was just not possible.

To compensate for that, Michael Okuda put these things in the script. Whenever there was a problem with the transporters, Geordi LaForge would mention something about the Heisenberg Compensators and everyone else on the ship would go "well of course the Heisenberg Compensators how silly of me." And somewhere in the world a quantum physicist would get a good giggle out of it.

The minds behind Star Trek were basically indicating to any viewers smart enough to know who Heisenberg was, that Star Trek's writers were gambling that by the 25th century, some smart geeky guy will figure out how to work around this particular law of quantum physics.