  We introduce a snapshot density matrix and snapshot spectrum for world-line
(WL) quantum Monte Carlo simulations, by integrating out the
continuous-imaginary-time index of WL snapshots. For the transverse-field Ising
chain, we reveal fundamental properties of the snapshot spectrum as follows.
(i) In the ordered phase, the isolated peak corresponding to the maximum
eigenvalue appears, indicating the classical nature of WL configurations. (ii)
In the disordered phase, the spectrum converges to the dome-like distribution
characterized by an effective aspect ratio of the snapshots. (iii) At the
critical point, the power-law distribution is observed with an appropriate
scaling analysis of the fixed aspect ratio. For the XXZ chain, we also obtain
numerical results consistent with the above properties. In addition, the
representation-basis dependence of the snapshot spectrum is also discussed.
