Redundant and synergistic coding in a driven nonlinear Bose-Hubbard dimer

We study the capability of a small quantum system to encode the temporal information of a classical driving signal (input time series) to explore if and when the whole of the system can encode more information than when each individual unit encodes the input information separately, i.e. synergistic coding. In particular, we theoretically and numerically investigate an information encoding capability of a Bose-Hubbard dimer driven by a time-dependent external field. We found that the growth of quantum correlation, as measured by the entanglement entropy, can lead to higher synergy (lower redundancy) of coding. We also study the classical limit of our model to investigate whether quantum correlation can enhance the information encoding capability. Our work suggests how to harness quantum entanglement to encode time-series data efficiently in a small, physically realizable quantum system.