Continuous variable dense coding under realistic non-ideal scenarios

We analyze the continuous variable (CV) dense coding protocol between a single sender and a single receiver when affected by noise in the shared and encoded states as well as when the decoding is imperfect. We derive a general formalism for the dense coding capacity (DCC) of generic two-mode Gaussian states. When the constituent modes are affected by quantum-limited amplifiers, pure-loss channels, and environmental interactions together with an inefficient decoding mechanism comprising imperfect double-homodyne detection, we investigate the pattern of DCC of the two-mode squeezed vacuum state (TMSV) by varying the strength of the noise. We further establish that the negative conditional entropy is responsible for providing quantum advantage in CV dense coding and identify a class of pure states capable of furnishing the maximal dense coding capacity equal to that of the TMSV under equal energy. We also demonstrate that, while the TMSV state provides the maximum quantum advantage in the DC protocol, there exists a class of states that is more resilient against noise than the TMSV state in the context of the DCC.