Experimental localisation of quantum entanglement through monitored classical mediator

Quantum entanglement is a form of correlation between quantum particles that cannot be increased via local operations and classical communication. It has therefore been proposed that an increment of quantum entanglement between probes interacting solely via mediator implies nonclassicality of the mediator. Indeed, under certain assumptions about the initial state, entanglement gain between the probes indicates quantum coherence in the mediator. Going beyond such assumptions, there exist other initial states which produce entanglement between the probes via only local interactions with the classical mediator. In this process the initial entanglement between any probe and the rest of the system "flows through" the classical mediator and gets localised between the probes. Here we demonstrate experimentally the growth of quantum correlations between two nuclear spin qubits interacting with a mediator qubit. The experimental realisation uses liquid-state NMR spectroscopy on dibromofluoromethane where carbon spin mediates interactions between hydrogen and fluorine spins. We additionally monitor, i.e. dephase, the mediator in order to emphasise its classical character. Quantum entanglement still gets localised through such monitored and classical mediator. Our results indicate necessity of verifying features of the initial state if entanglement gain between the probes is the figure of merit witnessing non-classical mediator. Such methods were proposed to have exemplary applications in quantum optomechanics, quantum biology and quantum gravity.