Attosecond
science offers unprecedented precision in probing the
initial moments of chemical reactions, revealing the dynamics of molecular
electrons that shape reaction pathways. A fundamental question emerges:
what role, if any, do quantum coherences between molecular electron
states play in photochemical reactions? Answering this question necessitates
quantum tomographythe determination of the electronic density
matrix from experimental data, where the off-diagonal elements represent
these coherences. The Maximal Entropy (MaxEnt) based Quantum State
Tomography (QST) approach offers unique advantages in studying molecular
dynamics, particularly with partial tomographic data. Here, we explore
the application of MaxEnt-based QST on photoexcited ammonia, necessitating
the operator form of observables specific to the performed measurements.
We present two methodologies for constructing these operators: one
leveraging Molecular Angular Distribution Moments (MADMs) which accurately
capture the orientation-dependent vibronic dynamics of molecules and
another utilizing Angular Momentum Coherence Operators to construct
measurement operators for the full rovibronic density matrix in the
symmetric top basis. A key revelation of our study is the direct link
between Lagrange multipliers in the MaxEnt formalism and the unique
set of MADMs. Additionally, we visualize the electron density within
the molecular frame, demonstrating charge migration across the molecule.
Furthermore, we achieve a groundbreaking milestone by constructing,
for the first time, the entanglement entropy of the electronic subsystema
metric that was previously inaccessible. The entropy vividly reveals
and quantifies the effects of coupling between the excited electron
and nuclear degrees of freedom. Consequently, our findings open new
avenues for research in ultrafast molecular spectroscopy within the
broader domain of quantum information science, offering profound implications
for the study of molecular systems under excitation using quantum
tomographic schemes.