States of a composite quantum system (e.g., bipartite ones) are described by density operators ρb(1, 2), which provide the possibility to construct reduced density operators ρb(1) = T r2ρb(1, 2), ρb(2) = T r1ρb(1, 2). They describe the states of the subsystems 1 and 2, respectively. As observed recently in [1]-[4] the quantum properties of systems without subsystems can be formulated by means of invertible map of integers 1, 2, 3 . . . onto pairs (triples, etc) of integers (i, k), j, k = 1, 2, . . .. The state density operator ρb1 of system without subsystems, e.g., the state of single qudit j = 0, 1/2, 1, 3/2, 2, . . . can be mapped onto density operator of the system containing the subsystems (e.g., the state of two qudits) ρb(1, 2). Thus, we can translate known properties of quantum correlations associated with structure of bipartite system like entanglement to the system without subsystems. We study the corresponding properties of the qudit and two-qubit systems in parallel. The separability and the entanglement of the qudit with j = 3/2 are defined. The explicit formulas for von Neumann entropy and information and, the entropic inequalities for X-states of the qudit with j = 3/2 are derived. Minkowski type inequalities [5] with one and two parameters are presented for such system without subsystems.