  When two quantum systems are coupled via a mediator, their dynamics has
traces of non-classical properties of the mediator. We show how this
observation can be effectively utilised to study the quantum nature of
materials without well-established structure. A concrete example considered is
Sr$_{14}$Cu$_{24}$O$_{41}$. Measurements of low temperature magnetic and
thermal properties of this compound were explained with long-range coupling of
unpaired spins through dimerised spin chains. We first show that the required
coupling is not provided by the spin chain alone and give alternative compact
two-dimensional spin structures compatible with the experimental results. Then
we argue that any mediator between the unpaired spins must share with them
quantum correlations in the form of quantum discord and in many cases quantum
entanglement. In conclusion, present data witnesses quantum mediators between
unpaired spins in Sr$_{14}$Cu$_{24}$O$_{41}$.
