  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
tomography: the 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. Furthermore, we achieve a groundbreaking milestone by constructing, for
the first time, the entanglement entropy of the electronic subsystem: a 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.
