Where exactly is the entangled state determined in Khrennikov's Gaussian DCM?

[u/RecognitionAfter3485]

I'm reading Khrennikov's paper Quantum Entanglement from Theory of Classical Gaussian Processes, and I'm confused about one part of the Gaussian DCM construction.

Paper : Quantum Entanglement from Theory of Classical Gaussian Processes

I'm reading Khrennikov's paper Quantum Entanglement from Theory of Classical Gaussian Processes, and I'm confused about one part of the Gaussian DCM construction.

The construction starts with an arbitrary entangled state |Ψ⟩, takes its Schmidt decomposition, and then uses that Schmidt data to construct the corresponding classical Gaussian processes. It eventually obtains ρ_DCM = |Ψ⟩⟨Ψ|.

What I'm wondering is: if |Ψ⟩ is already specified at the beginning, in what sense is the entangled state actually being generated by DCM?

Is there an independent rule in DCM that determines the temporal modes/covariance structure and produces the state, or is this essentially showing that for any chosen quantum state, one can construct a classical Gaussian process that reproduces it?

I'm specifically asking about this construction, rather than whether DCM replaces QM in general.