CDP: Non Classical Correlations at Spacelike Separation

[Point Conception]

Does the Cluster Decomposition Principle explain the spacelike non classical correlations in EPR experiments
without action at a distance ? With CDP defined : S α₁α₂β₁β₂ = S α₁β₁Sα₂β₂
Does this definition equate to the locality assumption : P(A,B|a,b,λ) = P (A|a,λ)P(B|b,λ)
If so then does the CDP equate to the Extended Causality described by @A. Neumaier and account for the non classical correlations with non separability, in part since separability is an EPR assumption ?

 

[A. Neumaier]

The Cluster Decomposition Principle in itself explains nothing. It is a property of observed asymptotic states and a result in relativistic quantum field theory; see Weinberg's Vol 1.

To derive extended causality one needs assumptions about relativistic causality. These are embodied classically in covariant actions leading to hyperbolic PDEs, and in QFT in the spacelike (anti)commutativity of causal fields.

To get from interacting fields individual particles (as used in EPR experiments) one needs to make approximations, since particles give a meaningful description only asymptotically (as scattering states), and hence only when they are approximately free for a sufficiently long time. Since extended causality is a property of solutions of classical PDEs, one should expect it to remain valid in the quantum case. But at present this is a conjecture only.