  Entanglement is a defining feature of quantum mechanics that can be a
resource in engineered and natural systems, but measuring entanglement in
experiment remains elusive especially for large chemical systems. Most
practical approaches require determining and measuring a suitable entanglement
witness which provides some level of information about the entanglement
structure of the probed state. A fundamental quantity of quantum metrology is
the quantum Fisher information (QFI) which is a rigorous witness of
multipartite entanglement that can be evaluated from linear response functions
for certain states. In this work, we explore measuring the QFI of molecular
exciton states of the first-excitation subspace from spectroscopy. In
particular, we utilize the fact that the linear response of a pure state
subject to a weak electric field over all possible driving frequencies encodes
the variance of the collective dipole moment in the probed state, which is a
valid measure for QFI. The systems that are investigated include the molecular
dimer, $N$-site linear aggregate with nearest-neighbor coupling, and $N$-site
circular aggregate, all modeled as a collection of interacting qubits. Our
theoretical analysis shows that the variance of the collective dipole moment in
the brightest dipole-allowed eigenstate is the maximum QFI. The optical
response of a thermally equilibrated state in the first-excitation subspace is
also a valid QFI. Theoretical predictions of the measured QFI for realistic
linear dye aggregates as a function of temperature and energetic disorder due
to static variations of the host matrix show that 2- to 3-partite entanglement
is realizable. This work lays some groundwork and inspires measurement of
multipartite entanglement of molecular excitons with ultrafast pump-probe
experiments.
