Fermionic entanglement that survives a black hole

TL;DR

This paper investigates how fermionic entanglement behaves under acceleration near a black hole, showing that despite multiple modes being excited, entanglement loss remains limited due to fermionic statistics, providing insights into the black hole information paradox.

Contribution

It relaxes the single mode approximation for fermions, demonstrating that entanglement survival is robust and independent of specific states or modes, unlike previous assumptions.

Findings

Entanglement loss is limited despite multiple excited modes.

Surviving entanglement is independent of initial state and mode number.

Fermionic statistics impose a structure that preserves some entanglement.

Abstract

We introduce an arbitrary number of accessible modes when analyzing bipartite entanglement degradation due to Unruh effect between two partners Alice and Rob. Under the single mode approximation (SMA) a fermion field only had a few accessible levels due to Pauli exclusion principle, conversely to bosonic fields which had an infinite number of excitable levels. This was argued to justify entanglement survival in the fermionic case in the SMA infinite acceleration limit. Here we relax SMA. Hence, an infinite number of modes are excited as the observer Rob accelerates, even for a fermion field. We will prove that, despite this analogy with the bosonic case, entanglement loss is limited. We will show that this comes from fermionic statistics through the characteristic structure it imposes on the infinite dimensional density matrix for Rob. Surprisingly, the surviving entanglement is independent of the specific maximally entangled state chosen, the kind of fermionic field analyzed, and the number of accessible modes considered. We shall discuss whether this surviving entanglement goes beyond the purely statistical correlations, giving insight concerning the black hole information paradox.