Comment on “Fermionic entanglement ambiguity in noninertial frames”

Abstract

In this comment we show that the ambiguity of entropic quantities calculated in [1] for fermionic fields in the context of Unruh effect is not related to the properties of anticommuting fields, as claimed in [1], but rather to wrong mathematical manipulations with them and not taking into account a fundamental superselection rule of quantum field theory. * Electronic address: kbradler@cs.mcgill.ca

Characterization of Unruh channel in the context of open quantum systems

“…This arises from the issues related to superselection rules, restricting the superpositions of bosons and fermions [54]. A careful use of the superselection rules is important for determining the class of states permissible for describing a composite system of, for e.g., two fermions [55][56][57][58]. Thus, for e.g., given a fermionic vacuum state |0, 0 , one could generate the states…”

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.…”

Convergence of fermionic-field entanglement at infinite acceleration in relativistic quantum information

“…The results of this brief report make clear that the procedure used by previous works in fermionic entanglement in noninertial frames has to be revised, but there is still a way to use this kind of fermion-qubit mapping without losing the physical results: even though the mapping of the fermionic Fock space to a qubit system does not respect the canonical anticommutation relations [13], it can be shown that it is a well-defined mathematical procedure, and the class of physical operator orderings can be rigorously identified [14].…”

“…That is, instead of considering the full fermionic system and take into account all the anticommutation signs that appear when computing the reduced state, these previous works would choose some operator ordering for defining the Fock basis and afterwards treat the system as a collection of qubits, with no anticommutation properties [1,13]. If not done carefully, this procedure introduces spurious signs which result in an unphysical behaviour for entanglement measures; in particular, there is no convergence of entanglement in the limit of infinite acceleration, as fig.…”

“…There has been a debate about what is the proper way to deal with fermions in Relativistic Quantum Information. After the publication of [1], a comment on this article appeared [13], and the arguments were contested in [14].…”