Fermionic-mode entanglement in quantum information

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 anticommutation relations are satisfied, e.g., in relativistic quantum fields or fermionic trapped ions. * pmxnf@nottingham.ac.uk

Renormalized entropy of entanglement in relativistic field theory

“…For critical systems, the correlation length diverges, hence different arguments are needed. For fermionic systems, an ambiguity in the definition of entanglement measures between subsystems arises due to the anticommutation of the creation and annihilation operators [33,34]. One can reformulate the problem of entanglement between localized subsystems in a purely algebraic way [15,16,[35][36][37], and a possible extension of the coarse-graining procedure to the algebraic framework is under investigation.…”

The Feynman problem and fermionic entanglement: Fermionic theory versus qubit theory

“…Despite its computational power, the jwt fails to solve completely the issue established by Feynman: physically local Fermionic operations are mapped into nonlocal quantum ones and vice versa. As noticed by many authors this can lead to ambiguities in defining the partial trace, [11][12][13][14] and in assessing the local nature of operations. 15 Independently on the jwt the Fermionic systems are usually assumed to obey the Wigner superselection rule.…”

Spectral properties of reduced fermionic density operators and parity superselection rule

“…We demonstrate that spectra of mode-reduced states do not necessarily coincide for a general fermionic state, which can be interpreted as a violation [24] of the Araki-Lieb inequality [25]. This fact should be taken into account when the entanglement of pure states is quantified via the entropy of one of subsystems [26]. The discrepancy between spectra (entropies) of subsystems of a pure state seems to be unphysical (since the result depends on labelling), so we further find necessary and sufficient conditions for spectra to be coincident for mode-reduced states.…”