On coding of a quantum source of states with a finite frequency band: Quantum analogue of the Kotelnikov theorem on sampling

An example of coding a source of quantum states with a finite frequency band $W$ and finite exit power not exceeding $\sim(\hbar W)\cdot W$ is given. The number of classical information bits that can be coded in the quantum states generated by such a source per unit time is $C=W$. Such a source is minimal in the sense that the filling factor for each of the orthogonal single-particle modes constituting $N=WT$-photon vector in time window $2T$ is equal to 1. This result can be treated as a quantum analogue of the Kotelnikov theorem on sampling for classical signals.