  Manipulating photon states serves as a primary requirement for various
optical devices and is of high relevance for quantum information technology.
Nevertheless, the fundamental theoretical framework for tens-of-photon states
has not been established. This study successfully establishes the
matrix-product-state theory to explore the statistics of the tens-of-photon
states scattered by optical cavities (OCs), two-level atoms (TLAs), and
Jaynes-Cummings emitters (JCEs) in waveguide-QED systems. Taking 10-photon
states as an example, we reveal some novel physical results that differ from
those for few-photon cases. We verify that OCs do not change the statistics of
the incident photon states, being independent of the photon number. However,
for the TLAs and JCEs, the photon number strongly impacts the photon bunching
and anti-bunching behaviors. As the photon number increases, there exists a
maximum strength for the photon-photon correlation induced by the JCE.
Especially, the scattered waves by the TLA (or JCE) exhibit extremely different
statistics behaviors for the 10-photon cases from those for the bi-photon.
These distinguishable conclusions for the tens-of-photon states and the
matrix-product-state theory pave the way for the multi-photon manipulation.
