  By embedding a $\cal PT$-symmetric (pseudo-Hermitian) system into a large
Hermitian one, we disclose the relations between $\cal{PT}$-symmetric
Hamiltonians and weak measurement theory. We show that the amplification effect
in weak measurement on a conventional quantum system can be used to effectively
simulate a local broken $\cal PT$-symmetric Hamiltonian system, with the
pre-selected state in the $\cal PT$-symmetric Hamiltonian system and its
post-selected state resident in the dilated Hamiltonian system.
