Discontinuities of the quantum Fisher information and the Bures metric

Dominik Šafránek

Published 2016-12-14Version 1

We show that two quantities in quantum metrology that were thought to be the same, the quantum Fisher information matrix and the Bures metric, are not the same. They differ at points at which an eigenvalue of the density matrix vanishes. The quantum Fisher information matrix is discontinuous at these points. However, these discontinuities are removable in some sense. We show that the expression given by the Bures metric represents the continuous version of the quantum Fisher information matrix. We also derive an explicit formula for the Bures metric for both singular and non-singular density matrices.