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arXiv:1205.0617 · Physical Review A

Entanglement amplification of fermionic systems in an accelerated frame

Younghun Kwon, Jinho Chang

Published Jul 3, 2012• 7 citations
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Abstract

In this Brief Report we present an analysis deriving physical results in the entanglement amplification of fermonic systems in the relativistic regime, that is, beyond the single-mode approximation. This leads a recent work by Montero and Mart\'{\i}n-Mart\'{\i}nez [J. High Energy Phys. 07 (2011) 006] to a physical result, and confirms that the phenomenon of entanglement amplification can actually happen in the relativistic regime.

DOI
10.1103/physreva.86.014302

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In this Brief Report we present an analysis deriving physical results in the entanglement amplification of fermonic systems in the relativistic regime, that is, beyond the single-mode approximation. This leads a recent work by Montero and Mart'{\i}n-Mart'{\i}nez [J. High Energy Phys. 07 (2011) 006] to a physical result, and confirms that the phenomenon of entanglement amplification can actually happen in the relativistic regime.
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.
In this paper, we investigate the behavior of bipartite entanglement of fermionic systems when one of the parties is traveling with a uniform acceleration. For the ordering problem in fermionic systems, we apply the recent result of Montero and Mart\'{\i}n-Mart\'{\i}nez [Phys. Rev. A 83, 052306 (2011)]. Based on the approach, we consider both pure and mixed entangled states, and we show that the behavior in terms of the entanglement measure (negativity) allows one to obtain physical results, i.e., its convergence in the infinite acceleration. The behavior shows that the ordering employed is relevant to derive physical results for fermionic entanglement. This also corrects the previous analysis of Mart\'{\i}n-Mart\'{\i}nez and Fuentes.
One of the defining features of quantum theory is entanglement, the notion that quantum systems can display correlations that are impossible from the classical \npoint of view. In quantum information theory entanglement has come to be recognised as a physical resource that enables new technologies that perform information \nprocessing tasks which are beyond the limits of the classical realm. It has been realised only recently that entanglement is dependent on the frame of reference in \nboth inertial and accelerated systems. In this thesis, we investigate the relativistic entanglement of massive spin-1=2 particles in inertial frames by focussing on the \ndependence of entanglement on the geometry of the underlying boost scenario. We first explore the ‘qubit’ of the relativistic setting: a single particle with spin and momentum, with momentum given by a Gaussian distribution. We study the system in a variety of different boost scenarios, analysing the behaviour of entanglement \nfrom a geometric point of view. The spin-spin entanglement of two particle systems is then surveyed for many different discrete product and entangled momenta, with the spins in the Werner state. We also extend the analysis to continuous momentum states and study them in a variety of geometries. The results obtained from the analysis of discrete states are applied to continuous states, leading to a better \nunderstanding of the behaviour of entanglement. We lastly discuss the common view according to which Lorentz boosts leave the total entanglement of the state invariant.
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.