We use polarization operators known from quantum theory of angular momentum to expand the N ×N dimensional density operators. Thereby, we construct generalized Bloch vectors representing density matrices. We study their properties and derive positivity conditions for any N. We also apply the procedure to study Bloch vector space for a qubit and a qutrit.

We proposed the procedure of measuring the unknown state of the three-level system – the qutrit, which was realized as the arbitrary polarization state of the single-mode biphoton field. This procedure is accomplished for the set of the pure states of qutrits; this set is defined by the properties of SU(2) transformations, that are done by the polarization transformers.

Qutrit (or ternary) structures arise naturally in many quantum systems, notably in certain non-abelian anyon systems. We present efficient circuits for ternary reversible and quantum arithmetics. Our main result is the derivation of circuits for two families of ternary quantum adders. The main distinction from the binary adders is a richer ternary carry which leads potentially to higher resourc...

We proposed the procedure of measuring the unknown state of the three-level system – the qutrit, which was realized as the arbitrary polarization state of the single-mode biphoton field. This procedure is accomplished for the set of the pure states of qutrits; this set is defined by the properties of SU(2) transformations, that are done by the polarization transformers.

A single qutrit with transitions selectively driven by weakly-coupled reservoirs can implement one of the world's smallest refrigerators. We analyze performance $N$ such fridges that are collectively coupled to reservoirs. observe a quantum boost, manifest in quadratic scaling steady-state cooling current $N$. As grows further, reduces linear, since responsible for boost become energetically un...

Considering generalized concurrence as the criterion of entanglement, we study entanglement properties of superposition of two qutrit coherent states, as a function of their amplitudes. These states may attain maximum entanglement or no entanglement at all, depending on the choice of the parameters involved. The states revealing maximum entanglement also display the maximum violations of the Be...