Abstract
The embedding of the -qubit space into the -fermion space with modes is a widely used method in studying various aspects of these systems. This simple mapping raises a crucial question: Does the embedding preserve the entanglement structure? It is known that the answer is affirmative for and . That is, under either local unitary (LU) operations or with respect to stochastic local operations and classical communication (SLOCC), there is a one-to-one correspondence between the two- (or three)-qubit orbits and the two- (or three)-fermion orbits with four (or six) modes. However, these results do not generalize as the mapping from the -qubit orbits to the -fermion orbits with modes is no longer surjective for . Here we consider the case of . We show that, surprisingly, the mapping of orbits from qubits to fermions is injective under SLOCC, and a similar result holds under LU for generic orbits. As a by-product, we obtain a complete answer to the problem of SLOCC equivalence of pure four-qubit states.
- Received 10 September 2013
DOI:https://doi.org/10.1103/PhysRevA.88.052309
©2013 American Physical Society