In modern physics search for invariants has turned out to be extremely useful. The notion of invariant includes sets of properties that do not change under variation of modes of observation and description as defined by the invariant. Invariants imply symmetries. Therefore, physicists attribute to invariants an "absoluteness", differing them from other concepts, equations, properties etc. Referring to the invariants in question, they build up theoretical models making it possible to consistently explain their observations. The lack of such generally accepted invariants and principles which can serve as the foundation of the quantum theory is certainly the main reason for the problem of understanding and interpreting quantum physics. In the present paper we find an operational quantum information invariant that reflects the intrinsic symmetry of the underlying Hilbert space of the system.