I am sure you love scrambled eggs for breakfast. They can be a good way to start in the morning!
Have you heard of "scramble" in another context? Scramble means to mix up, shuffle, melee; in general, you scramble something when it becomes disorganized, chaotic, leading to a lose of information.
In physics, it has been conjectured that black holes are the fastest scramblers in nature [link1, link2], as any information thrown into them is "scrambled" with what is inside, and then is released very fast (emission known as Hawking radiation). This also called "Butterfly effect" indicates that an initial perturbation induces the spreading of information and a growth of chaos. There is a lot of research going on about the role of scrambling in black holes, string theory and the connection with quantum gravity. One example can be found here.
The next step leads us to thermodynamics, as thermal systems are considered chaotic as well. The phenomenon of thermalization (the process of physical bodies reaching thermal equilibrium through mutual interaction) is very sensitive to the initial conditions. Now we start to see a link with the process of scrambling in black holes described above.
We are now ready to understand the link at the quantum level. If we look at the process of thermalization in a quantum system, it is the same as to understand the spreading of information, or in other words, how the system scrambles. The out-of-time-order correlators (OTOC) are used to measure quantum chaos, and therefore many of the current experiments (to know more click on the image below) focus on trying to measure these correlators through non local measurements. The idea is to be able to set a time scale on which black holes should start releasing information. And to make everything even harder to understand, it seems in the process of scrambling time flows in both directions!
All in all, the important concepts are here. Furthermore, any additional information can be found in the links provided.
In summary, any information falling into a black hole gets scrambled and the released of radiation that follows could be key to understand quantum gravity.
It is like putting milk into your coffee, mixing them (process of thermalization), and then you are trying to understand where the milk comes from, although everything is already light brownish and you have no means to access the initial white milk.
As it is not possible to study black holes in the lab, the idea is use many-body quantum physics and quantum chaos, by studying thermalization in a bunch of atoms (spins) through these out-of-time correlators, thus suggesting a table-top simulation for quantum gravity.