Convergence of fermionic-field entanglement at infinite acceleration in relativistic quantum information

We provide a simple argument showing that in the limit of infinite acceleration, the entanglement in a fermionic-field bipartite system must be independent of the choice of Unruh modes. This implies that most tensor product structures used previously to compute field entanglement in relativistic quantum information cannot give rise to physical results.

Figure 1

Minkowski spacetime diagram showing the world lines of an inertial observer Alice, and one uniformly accelerated observer moving hyperbolically in region I. Note that regions I and II are causally disconnected from each other.

Figure 2

Negativity as a function of $r$ for the state (3) with $P=Q=1/\sqrt{2}$, $a_1=b_2=1$, $a_2=b_1=0$. The blue solid lines correspond to the physical ordering of [1], whereas the red dashed lines reproduce the results of [9] where the very same field state was analyzed employing the unphysical operator ordering used in [9, 10, 12].