State estimation from pair of conjugate qudits
  We show that, for $N$ parallel input states, an anti-linear map with respect to a specific basis is essentially a classical operator. We also consider the information contained in phase-conjugate pairs $|\phi > |\phi^*>$, and prove that there is more information about a quantum state encoded in phase-conjugate pairs than in parallel pairs. 
Xiang-Fa Zhou, Yong-Sheng Zhang, Guang-Can Guo