Entanglement generation through particle detection in systems of identical fermions

Abstract

We investigate the generation of entanglement in systems of identical fermions through a process involving particle detection, focusing on the implications that these kindsof 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. The aim of this scheme is to generate states with a definite number of particles at two separated locations, that can effectively be described as entangled states of two distinguishable qubits, starting from an initial pure state of two indistinguishable fermions exhibiting correlations purely due to antisymmetrization. It is argued that the proposed extraction of a useful entanglement-based resource, given by two distinguishable qubits entangled in the standard sense, does not contravene the notion of entanglement in identical-fermion systems as describing correlations beyond those purely due to their indistinguishability. In point of fact, it is shown that this concept of entanglement, here referred to as fermionic entanglement, actually helps to clarify some essential aspects of the entanglement generation process. In particular, we prove that the amount of entanglement exhibited by the above mentioned pair of distinguishable qubits, obtained after post-selection of a state having a definite number of particles in two separated locations, equals the amount of fermionic entanglement created by this 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 fermionic entanglement, but actually reinforces it.