The Methodology of Quantum Key Distributions Systems

1. Existing Products

I've not yet come across commercial systems using entanglement based schemes. The commercial products I've seen, like ID Quantique and MagiQ seem to be using BB84/B92 type protocols. It may be relevant to the question to note that I'm only aware of these particular companies because their commercial QKD systems got hacked.

The infrastructure for long distance entanglement on a commercial scale doesn't exist yet. There's a lot of money going into it, but the no cloning theorem makes quantum repeater design highly non-trivial, and a robust solution has not yet emerged.

If you're willing to consider government activity (which will certainly have a commercial aspect), China has accomplished satellite-based QKD that utilizes entanglement. The last I checked, data rates were still in the 10's of kbit/s and operation was dependent on favorable atmospheric conditions. It's a remarkable achievement, but it's still early stage.

2. Methods

Based on the information I've seen, the high-level scheme used in the satellite-based QKD with entanglement noted above is as follows:

1. The satellite generates entangled photon pairs and directs half of each pair to two geographically separated parties.
2. The two parties use incoming entangled photon pairs to perform a CHSH test.
3. The parties classically/publicly communicate regarding measurement bases used during the test (critically there is no public discussion of measurement outcomes).
4. Based on each party's private measurement outcome data and collective basis information, the parties determine whether the CHSH inequality was violated.
5. In the case of CHSH inequality violation, entanglement is validated and the parties have private data sets that are correlated beyond classical limits. The parties then use these correlated data sets to generate a set of one-time pads.

Note that this scheme relies on entanglement, but not teleportation. Entanglement is, independently, a very valuable resource in QKD. Teleportation schemes pose some additional technical challenges, and may be bit further out.