On Capacity of a Quantum Communications Channel

An example is constructed that shows that the additive property $C_{n+m}=C_n+C_m$ that is characteristic of the capacities in classical information theory need not obtain for a quantum communications channel. In view of this, the definition itself of capacity of a quantum communications channel is in need of refinement. By using the property of subadditiveness, $C_{n+m}\leq C_n+C_m$, which is maintained in the quantum case, it is natural to define the capacity as $C=\lim_{n\to\infty}C_n/n$. Generally speaking, $C>C_1$ in this case. An analog of the classical coding theorem obtains for $C$. Some bounds are obtained for the capacity $C$.