  A quantum system can be monitored through repeated interactions with meters,
followed by their detection. The state of the system at time t is thus
conditioned on the information obtained until that time. More insight in the
state dynamics is provided, however, by the past quantum state (PQS) [S.
Gammelmark et al. Phys. Rev. Lett. 111, 160401 (2013)]. It relies on all
aspects of the system evolution which are recorded in the past and in the
future of t. Using PQS analysis for the quantum non-demolition photon number
counting in a cavity, we can reveal information hidden in the standard approach
and resolve a wider range of number states. This experiment demonstrates the
strong potential of PQS analysis.
