Universal and Maximal Entanglement Swapping in General Fermionic Gaussian States

TL;DR

This paper demonstrates a universal method for achieving maximal entanglement swapping in fermionic Gaussian states through projective Bell measurements, independent of initial states, revealing a new fermionic route to measurement-induced entanglement.

Contribution

It introduces a universal entanglement swapping mechanism in fermionic Gaussian states, exactly derived for general particle-number-conserving states, and highlights the role of fermionic statistics and Gaussianity.

Findings

Post-measurement state factorizes into Bell pairs

Maximal entanglement is independent of initial states

Numerical simulations confirm the theoretical results

Abstract

Exploring universal entanglement structure in many-body systems is both fundamental and challenging, particularly when the system undergoes non-unitary operations. In this work, we uncover a universal mechanism for realizing maximal entanglement swapping in fermionic Gaussian states subjected to projective Bell measurements. We consider two initially decoupled, half-filled copies of a free-fermion system in arbitrary dimensions and perform post-selective Bell measurements on half of the corresponding sites across the two copies. Remarkably, the post-measurement state factorizes into a product of Bell pairs, establishing maximal interlayer entanglement entirely independent of the initial Gaussian state. We derive this post-measurement state exactly for general particle-number-conserving fermionic Gaussian states, establishing both the validity and universality of the mechanism, with numerical simulations serving as consistency checks. This phenomenon arises from a robust interplay between fermionic statistics and Gaussianity, revealing a distinct fermionic route to measurement-induced maximal entanglement.