Sharply Bounding the Holevo Quantity
Lin Zhang, Junde Wu, Shao-Ming Fei · arXiv (Cornell University) · 2011
For a quantum ensemble $\cE_3 =\set{\Pa{p_i,\rho_i}}_{i=1}^3$, M. Fannes \emph{et al.} conjectured that the entropy of the correlation matrix of $\cE_3 =\set{\Pa{p_i,\rho_i})}_{i=1}^3$ is upper bound for the Holevo quantity $\chi\Pa{\cE_3}$ of quantum ensemble $\cE_3 =\set{\Pa{p_i,\rho_i}}_{i=1}^3$. In this paper, we prove the conjecture under a strictly constraint condition.