  The problem of how measurement in quantum mechanics takes place has existed
since its formulation. Von Neumann proposed a scheme where he treated
measurement as a two-part process -- a unitary evolution in the full
system-ancilla space and then a projection onto one of the pointer states of
the ancilla (representing the "collapse" of the wavefunction). The Lindblad
master equation, which has been extensively used to explain dissipative quantum
phenomena in the presence of an environment, can effectively describe the first
part of the von Neumann measurement scheme when the jump operators in the
master equation are Hermitian. We have proposed a non-Hermitian Hamiltonian
formalism to emulate the first part of the von Neumann measurement scheme. We
have used the embedding protocol to dilate a non-Hermitian Hamiltonian that
governs the dynamics in the system subspace into a higher-dimensional Hermitian
Hamiltonian that evolves the full space unitarily. We have obtained the various
constraints and the required dimensionality of the ancilla Hilbert space in
order to achieve the required embedding. Using this particular embedding and a
specific projection operator, one obtains non-Hermitian dynamics in the system
subspace that closely follow the Lindblad master equation. This work lends a
new perspective to the measurement problem by employing non-Hermitian
Hamiltonians.
