  We theoretically study operations with a four-level superconducting circuit
as a two-qubit system. Using a mapping on a two-qubit system, we show how to
implement iSWAP gates and Hadamard gates through pulses on transitions between
particular pairs of energy levels. Our approach allows one to prepare pure
two-qubit entangled states with desired form of reduced density matrices of the
same purity and, in particular, arbitrary identical reduced states of qubits.
We propose using schemes for the Hadamard gate and two-qubit entangled states
with identical reduced density matrices in order to verify $\log{N}$
inequalities for Shannon and R\'enyi entropies for the considered noncomposite
quantum system.
