# Bipartite entanglement in fermion systems

## TL;DR

This paper explores the relationship between fermion entanglement and bipartite entanglement, showing how fermionic states can serve as resources for quantum teleportation and superdense coding, with implications for quantum information processing.

## Contribution

It establishes a connection between fermion entanglement and bipartite entanglement, including a method to quantify and utilize fermionic entanglement in quantum protocols.

## Key findings

- Exact correspondence between fermion and bipartite entanglement under certain conditions
- Fermionic entanglement can quantify entanglement between distinguishable qubits
- Fermionic entanglement provides a lower bound for bipartition entanglement

## Abstract

We discuss the relation between fermion entanglement and bipartite entanglement. We first show that an exact correspondence between them arises when the states are constrained to have a definite local number parity. Moreover, for arbitrary states in a four dimensional single-particle Hilbert space, the fermion entanglement is shown to measure the entanglement between two distinguishable qubits defined by a suitable partition of this space. Such entanglement can be used as a resource for tasks like quantum teleportation. On the other hand, this fermionic entanglement provides a lower bound to the entanglement of an arbitrary bipartition although in this case the local states involved will generally have different number parities. Finally the fermionic implementation of the teleportation and superdense coding protocols based on qubits with odd and even number parity is discussed, together with the role of the previous types of entanglement.