The qudit state for j = 3/2 with density matrix of the form corresponding to X-state of two-qubits is studied from the point of view of entanglement and separability properties. The method of qubit portrait of qudit states is used to get the entropic inequalities for the entangled state of the single qudit. The tomographic probability representation of the qudit X-state under consideration and its Shannon and q-entropic characteristics are presented in explicit form.
A novel recipe for exactly solving in finite terms a class of special differential Riccati equations is reported. Our procedure is entirely based on a successful resolution strategy quite recently applied to quantum dynamical time-dependent SU(2) problems. The general integral of exemplary differential Riccati equations, not previously considered in the specialized literature, is explicitly determined to illustrate both mathematical usefulness and easiness of applicability of our proposed treatment. The possibility of exploiting the general integral of a given differential Riccati equation to solve an SU(2) quantum dynamical problem, is succinctly pointed out.
Entropic inequalities related to the quantum mutual information for bipartite system and tomographic mutual information is studied for Werner state of two qubits. Quantum correlations corresponding to entanglement properties of the qubits in Werner state are discussed.
The phenomenon of quantum steering and probabilistic meaning of the correlations are discussed for the state of the single qudit. The method of qubit portrait of the qudit states is used to extend the known steering detection inequality to the system without subsystems. The example of the X-state with j = 3/2 is studied in detail.
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