Entanglement detection via subsystem quantum Fisher information
Phys. Rev. A 114, 032443 – Published 18 September, 2026
DOI: https://doi.org/10.1103/kxxy-llb2
Abstract
Quantum Fisher information (QFI) provides powerful entanglement criteria, but existing formulations are all related to the global QFI of the full composite state. We first define the block-diagonal postmeasurement ensemble obtained by local projective measurements on one subsystem of a bipartite state. Then we show that the QFI of the block-diagonal postmeasurement ensemble can decompose into the QFI of the unmeasured subsystem and the classical Fisher information of the measurement outcomes. For separable states the sum of the subsystem QFI and the classical Fisher information admits an upper bound expressed solely in terms of local variances; violation of this bound signals entanglement. Compared with Tóth's global spin-squeezing criterion [Phys. Rev. A 85, 022322 (2012)], our witness detects entanglement over a wider parameter range for high-dimensional systems. The dimensional advantage and reduced experimental cost make the subsystem QFI a practical entanglement witness.
