  Quantum Fisher information matrix (QFIM) is a cornerstone of modern quantum
metrology and quantum information geometry. Apart from optimal estimation, it
finds applications in description of quantum speed limits, quantum criticality,
quantum phase transitions, coherence, entanglement, and irreversibility. We
derive a surprisingly simple formula for this quantity, which, unlike
previously known general expression, does not require diagonalization of the
density matrix, and is provably at least as efficient. With a minor
modification, this formula can be used to compute QFIM for any
finite-dimensional density matrix. Because of its simplicity, it could also
shed more light on the quantum information geometry in general.
