Fermionic mode entanglement in quantum information

TL;DR

This paper develops a formalism for analyzing fermionic modes as quantum information carriers, clarifying their differences from qubits and addressing the ambiguities in defining subsystems without a tensor product structure.

Contribution

It introduces a density operator formalism on Fock space for fermionic modes and discusses the limitations of comparing them to qubits, resolving ambiguities in subsystem definitions.

Findings

Formalism unambiguously defines subsystems for fermionic modes

Fermionic modes differ fundamentally from qubits in quantum information

Results applicable to relativistic quantum fields and fermionic ions

Abstract

We analyze fermionic modes as fundamental entities for quantum information processing. To this end we construct a density operator formalism on the underlying Fock space and demonstrate how it can be naturally and unambiguously equipped with a notion of subsystems in the absence of a global tensor product structure. We argue that any apparent similarities between fermionic modes and qubits are superficial and can only be applied in limited situations. In particular, we discuss the ambiguities that arise from different treatments of this subject. Our results are independent of the specific context of the fermionic fields as long as the canonical anti-commutation relations are satisfied, e.g., in relativistic quantum fields, or fermionic trapped ions.