How can quantum field operators encode entanglement?

Abstract

We present techniques to construct the Deutsch–Hayden representation for quantum field operators and apply them to an entangled state of identical nonrelativistic spin-1/2 fermions localized in well-separated spatial regions. Using these entangled field operators we construct operators measuring spin in localized spatial regions, and verify that matrix elements of the spin-measurement operators in the information-free Deutsch–Hayden state yield the expected correlations between pairs of both entangled and unentangled particles. The entangled Deutsch–Hayden representation field operators furnish an explicitly separable description of the entangled system.