When quantum memory is useful for dense coding

We discuss dense coding with $n$ copies of a specific preshared state between the sender and the receiver when the encoding operation is limited to the application of group representation. In this problem, if the receiver keeps the quantum system of a part of preshared states, the receiver needs quantum memory. Depending on available encoding unitary operations, we investigate what preshared state offers an advantage of using quantum memory on the receiver's side.