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Are states of entanglement particles defined at their creation?

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    $\begingroup$ A pair (or larger set) of entangled particles is quantum system like any other quantum system, so its state evolves over time in accordance with the Schrodinger equation. $\endgroup$
    – gandalf61
    Commented Sep 7 at 10:30

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We often create pairs of entangled particles by creating them together. For example the archetypal experiment would be to create a particle anti-particle pair, let them separate then demonstrate entanglement by measuring their properties separately.

However this is done for experimental convenience, and particles do not need to be created together to be entangled. Any two systems that interact will form an entangled system even if they have never met before. Entanglement just means we cannot write the wave function of the whole system as a product of the wavefunctions of the two parts i.e.

$$ \Psi_{\mathrm{total}} \ne \psi_1\psi_2 $$

The wave function only factors like this if systems $1$ and $2$ are completely non-interacting, and any interaction between them will cause them to become entangled.

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