Entanglement witness derived from NMR superdense coding

It is shown that superdense coding (SDC) experiments by means of nuclear magnetic resonance (NMR) can show non-classical efficiency gain over classical communication only for nuclear spin polarization beyond a certain threshold, and this threshold coincides with that for non-separability of the density matrix. It is also claimed that transfer of two-bit information mediated by a single qubit in the previous NMR SDC experiments with low nuclear spin polarization is not ascribed to the non-classical effect induced by entanglement, but merely to a statistical effect in an ensemble system having a large number of molecules. Towards experimental detection of entanglement, a new class of entanglement witnesses is proposed, which is based on the measurement of nuclear spin magnetizations in the Bell basis and is suitable for actual NMR experiments.