Does disentanglement of a bipartite entanglement between systems A and B entail actual breaking of this bipartite entanglement or is it rather the beginning of a tripartite entanglement between A, B, and Environment?

I've only found examples of the latter in the literature (for both asymptotic disentanglement and entanglement sudden death). In these cases, the relationship between A and B didn't really end; it just became more complex and more difficult to describe fully because experimenters usually lacked the part of the information encoded in the environment after decoherence.

Are there any examples of mechanisms that simply break the bipartite entanglement between A and B without entangling them with anything else?


Yes, one can break entanglement without getting entangled with something else.

Consider e.g. two spins interacting via the Heisenberg interaction $\vec S_1\cdot \vec S_2$, which are initially in a state $\lvert\uparrow,\downarrow\rangle$. As time evolves, the system first gets entangled, and subsequently gets disentangled again, without any other system being involved. It is thus perfectly possible to disentangle two entangled qubits without involving any other system.


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