  Quantum learning (in metrology and machine learning) involves estimating
unknown parameters from measurements of quantum states. The quantum Fisher
information matrix can bound the average amount of information learnt about the
unknown parameters per experimental trial. In several scenarios, it is
advantageous to concentrate information in as few states as possible. Here, we
present two "go-go" theorems proving that negativity, a narrower
nonclassicality concept than noncommutation, enables unbounded and lossless
distillation of Fisher information about multiple parameters in quantum
learning.
