A Note on Holevo Quantity of SU(2)-invariant States

The Holevo quantity and the SU(2)-invariant states have particular importance in quantum information processing. We calculate analytically the Holevo quantity for bipartite systems composed of spin-j and spin-1/2 subsystems with SU(2) symmetry, when the projective measurements are performed on the spin-1/2 subsystem. The relations among the Holevo quantity, the maximal values of the Holevo quantity and the states are analyzed in detail. In particular, we show that the Holevo quantity increases in the parameter region F < F-d and decreases in region F > F-d when j increases, where F is function of temperature in thermal equilibrium and F-d = j/(2j + 1), and the maximum value of the Holevo quantity is attained at F = 1 for all j. Moreover, when the dimension of system increases, the maximal value of the Holevo quantity decreases.

Automated summary

The importance of Holevo quantity and SU(2)-invariant states in quantum information processing is explored. The analytical calculation of Holevo quantity for bipartite systems composed of spin-j and spin-1/2 subsystems with SU(2) symmetry is performed, specifically when projective measurements are conducted on the spin-1/2 subsystem. The relationships between Holevo quantity, its maximal values, and the states are analyzed in detail. The study reveals that the Holevo quantity increases in a certain parameter region and decreases in another as the spin-j increases. The maximum value of the Holevo quantity is achieved at a specific parameter value, and it decreases as the dimension of the system increases.