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.