Entanglement already exists in a state prior to measurement. It is not created by a measurement. Instead, it is always created locally by some nonlinear process or interaction. The entangled particles can then be separated so that there is a large distance between them.

One way to think of non-realism, is as the notion that there does not exist a unique reality. This notion is revealed by the typical expression of an entangled state, consisting of a superposition. For example $$ |\psi\rangle = \frac{1}{\sqrt{2}} (|U\rangle_A|V\rangle_B+|V\rangle_A|U\rangle_B) . $$ Each of the terms represents a "reality." When a measurement in the $A$ system produced a result $U$ it implies that the first term represents the manifested reality, for which the measurement in the $B$ system will produce $V$. At no point did we need to do or assume anything nonlocal.

Entanglement already exists in a state prior to measurement. It is not created by a measurement. Instead, it is always created locally by some nonlinear process or interaction. The entangled particles can then be separated so that there is a large distance between them.

One way to think of non-realism, is as the notion that there does not exist a unique reality. This notion is revealed by the typical expression of an entangled state, consisting of a superposition. For example $$ |\psi\rangle = \frac{1}{\sqrt{2}} (|U\rangle_A|V\rangle_B+|V\rangle_A|U\rangle_B) . $$ Each of the terms represents a "reality." When a measurement in the $A$ system produced a result $U$ it implies that the first term represents the pertinent reality, for which the measurement in the $B$ system will produce $V$. At no point did we need to do or assume anything nonlocal.