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We study the primary entanglement effect on the decoherence of reduced-density matrices
of scalar fields, which interact with other fields or independent mode functions. We study the (leading)
tree-level evolution of the scalar bispectrum due to a coupling between two scalar fields. We show
that the primary entanglement has a significant role in the decoherence of the given quantum state.
We find that the existence of such an entanglement could couple dynamical equations coming from a
SchrÃÂ¶dinger equation. We show that if one wants to see no effect of the entanglement parameter in
the decohering of the quantum system, then the ground state eigenvalues of the interaction terms in
the Hamiltonian cannot be independent of each other Generally, including the primary entanglement
destroys the independence of the interaction terms in the ground state. We show that the imaginary
part of the entanglement parameter plays an important role in the decoherence process without
posing any specific restriction to the interaction terms. Our results could be generalized to every
scalar quantum field theory with a well-defined quantization of its fluctuations in a given curved
space-time.
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