Quantum entanglement is one the most amazing phenomena in quantum mechanics. Moreover, research conducted in the last 20 years showed that the structure of quantum entanglement for many-body systems can be described using the (classical) geometric formalism.
For discrete systems, the formalism is provided by the so-called tensor networks. In the continuous case, as indicated by the famous AdS/CFT correspondence, the entanglement structure can be described in the language of differential geometry. A hypothetical possibility that arises from these considerations is characterization of the gravitational interaction as a result of the quantum entanglement.
Is this the fundamental nature of gravity? We would like to contribute to the answer to this fascinating question within our research as well. The first step in this direction is the paper Gauge fields and quantum entanglement, exploring the relation between entangled states and so-called holonomies of the SU(2) gauge field. The latter is, in particular, a building block of Loop Quantum Gravity.