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arXiv:1104.2307 · Physical Review A

Fermionic entanglement ambiguity in noninertial frames

Miguel Montero, Eduardo Martín-Martínez

Published Jun 16, 2011• 70 citations
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Abstract

We analyze an ambiguity in previous works on entanglement of fermionic fields in noninertial frames. This ambiguity, related to the anticommutation properties of field operators, leads to nonunique results when computing entanglement measures for the same state. We show that the ambiguity disappears when we introduce detectors, which are in any case necessary as a means to probe the field entanglement.

DOI
10.1103/physreva.83.062323

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In this Comment we show that the ambiguity of entropic quantities calculated by Montero and Mart\'{\i}n-Mart\'{\i}nez [Phys. Rev. A 83, 062323 (2011)] for fermionic fields in the context of the Unruh effect is not related to the properties of anticommuting fields, as claimed therein, but rather to wrong mathematical manipulations with them and not taking into account a fundamental superselection rule of quantum field theory.

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We show that, contrary to the claims of the preceding Comment [Br\'adler and J\'auregui, Phys. Rev. A 85, 016301 (2012)], our original work [Phys. Rev. A 83, 062323 (2011)] is devoid of flaws or mistakes. We show that the criticism comes from a misunderstanding of part of our work.

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We analyze an ambiguity in previous works on entanglement of fermionic fields in noninertial frames. This ambiguity, related to the anticommutation properties of field operators, leads to nonunique results when computing entanglement measures for the same state. We show that the ambiguity disappears when we introduce detectors, which are in any case necessary as a means to probe the field entanglement.
We generalize the study of fermionic and bosonic entanglement in noninertial frames to fields of arbitrary spin and beyond the single-mode approximation. After the general analysis we particularize for two interesting cases: entanglement between an inertial and an accelerated observer for massless fields of spin 1 (electromagnetic) and spin 3/23/23/2 (Rarita-Schwinger). We show that, in the limit of infinite acceleration, no significant differences appear between the different spin fields for the states considered.
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.