A Lower Bound on the C-Numerical Radius of Nilpotent Matrices Appearing in Coherent Spectroscopy
Chi-Kwong Li, Hugo J. Woerdeman · SIAM Journal on Matrix Analysis and Applications · 2005
We provide a lower bound for the efficiency of polarization or coherence transfer between quantized states under unitary transformations. Mathematically the problem is the determination of the C-numerical radius of A for certain nilpotent matrices C and A. The presented lower bound is conjectured to be exact as it coincides with numerical data provided in [U. Helmke et al., J. Global Optim., 23 (2002), pp. 283-308].