Measurement uncertainty and dense coding in a two-qubit system: Combined effects of bosonic reservoir and dipole–dipole interaction

The uncertainty principle imposes a limitation on the measurement accuracy of two incompatible observables and has potential applications in quantum information science. We explore the bipartite entropic uncertainty relation and dense coding for two qubits coupled via dipole–dipole interaction and subject to a bosonic reservoir. It is shown that there exists a trade-off between the uncertainty bound and the dense coding capacity which results in their opposite dynamical behaviors. Moreover, the behaviors of the measurement uncertainty and the dense coding capacity rely crucially on the initial system–reservoir correlation, the strength of the dipole–dipole interaction, and the degree of non-Markovianity, and one can reduce the measurement uncertainty and enhance the dense coding capacity by tuning these parameters to appropriate values.