Entanglement generation through particle detection in systems of identical fermions

TL;DR

This paper explores how entanglement can be generated and understood in systems of identical fermions through detection processes, clarifying the concept of fermionic entanglement and its relation to particle indistinguishability.

Contribution

It introduces a scheme for entanglement generation in fermions via splitting and detection, and demonstrates the equivalence between accessible and fermionic entanglement in this context.

Findings

Accessible entanglement equals fermionic entanglement created during detection.

The scheme generalizes to N-fermion systems of arbitrary dimension.

Entanglement generation aligns with the concept of fermionic entanglement, reinforcing its validity.

Abstract

We investigate the generation of entanglement in systems of identical fermions through a process involving particle detection, focusing on the implications that this kind of processes have for the concept of entanglement between fermionic particles. As a paradigmatic example we discuss in detail a scheme based on a splitting-plus-detection operation. This scheme generates states with accessible entanglement starting from an initial pure state of two indistinguishable fermions exhibiting correlations due purely to antisymmetrization. It is argued that the proposed extraction of entanglement does not contravene the notion that entanglement in identical-fermion systems requires correlations beyond those purely due to their indistinguishability. In point of fact, it is shown that this concept of entanglement, here referred to as {\it fermonic entanglement}, actually helps to clarify some essential aspects of the entanglement generation process. In particular, we prove that the amount of extracted accessible entanglement equals the amount of fermionic entanglement created with the detection process. The aforementioned scheme is generalized for the case of $N$-identical fermion systems of arbitrary dimension. It transpires from our present discussion that a proper analysis of entanglement generation during the splitting-plus-detection operation is not only consistent with the concept of fermonic entanglement, but actually reinforces this concept.