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arXiv:1201.1045 · Physical Review A

Comment on “Fermionic entanglement ambiguity in noninertial frames”

Kamil Brádler, Rocío Jáuregui

Published Jan 17, 2012• 29 citations
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Abstract

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.

DOI
10.1103/physreva.85.016301

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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.
We describe two problems current relativistic quantum information suffers from. The first point is an explanation of an alleged ambiguity of entropic quantities detected in a number of publications and incorrectly resolved in [M. Montero and E. Martin-Martinez, Physical Review A 83, 062323 (2011)]. We found that the problem arises due to wrong algebraic manipulations with fermions and ignoring the superselection rule for bosons and fermions. This leads to a misinterpretation of certain entropic quantities when applied to fermion fields. The second discussed point is to alert to a conceptual misunderstanding of the role of entanglement (and quantum correlations in general) in some of the studied relativistic scenarios. Instead, we argue in favor of investigating capacities of quantum channels induced by the relevant physical processes as dictated by quantum Shannon theory.
The characterization of entanglement is a fundamental issue for Quantum Information Theory. But the definition of entanglement depends on the notion of locality, and thus on the tensor product structure of the state space of the composite system. This notion is affected by the presence of superselection rules that restrict the accessible Hilbert space to a direct sum of subspaces. Indistinguishability of particles imposes one such restriction, namely to totally symmetric or totally antisymmetric states. The entanglement can in this case be defined with respect to partitions of modes in the second quantization formalism. For fermionic systems the Fock space of m modes is isomorphic to the space of m qubits, but the action of creation and annihilation operators is not local, due to their anticommutation. Conservation of the parity of fermion number imposes another relevant superselection rule. It requires that local physical observables commute with the local parity operator. Taking into account the considerations above, it is possible to define the set of separable states or equivalently the concept of entanglement for fermionic systems in a number of ways. Here we analyze systematically these possibilities and the relation among the various sets of separable states. We also discuss the behavior of the different classes when taking several copies of the state, as well as the characterization of the sets in terms of the usual criteria regarding the tensor product.