  We point out that realization of quantum communication protocols in
programmable quantum computers provides a deep benchmark for capabilities of
real quantum hardware. Particularly, it is prospective to focus on measurements
of entropy-based characteristics of the performance and to explore whether a
"quantum regime" is preserved. We perform proof-of-principle implementations of
superdense coding and quantum key distribution BB84 using 5- and 16-qubit
superconducting quantum processors of IBM Quantum Experience. We focus on the
ability of these quantum machines to provide an efficient transfer of
information between distant parts of the processors by placing Alice and Bob at
different qubits of the devices. We also examine the ability of quantum devices
to serve as quantum memory and to store entangled states used in quantum
communication. Another issue we address is an error mitigation. Although it is
at odds with benchmarking, this problem is nevertheless of importance in a
general context of quantum computation with noisy quantum devices. We perform
such a mitigation and noticeably improve some results.
