In complex time-consuming computations, we rarely have uninterrupted access to a high performance computer: usually, in the process of computation, some interruptions happen, so we need to store intermediate results until computations resume. To decrease the probability of a mistake, it is often necessary to run several identical computations in parallel, in which case several identical intermediate results need to be stored. In particular, for quantum computing, we need to store several independent identical copies of the corresponding qubits -- quantum versions of bits. Storing qubit states is not easy, but it is possible to compress the corresponding multi-qubit states: for example, it is possible to store the resulting 3-qubit state by using only two qubits. In principle, there are many different ways to store the state of 3 independent identical qubits by using two qubits. In this paper, we show that the current algorithm for such storage is uniquely determined by the natural symmetry requirements.