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arXiv:1111.6070 · Physical Review A

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

Miguel Montero, Eduardo Martín-Martínez

Published Feb 13, 2012• 31 citations
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Abstract

We provide a simple argument showing that in the limit of infinite acceleration, the entanglement in a fermionic-field bipartite system must be independent of the choice of Unruh modes. This implies that most tensor product structures used previously to compute field entanglement in relativistic quantum information cannot give rise to physical results.

DOI
10.1103/physreva.85.024301

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We provide a simple argument showing that in the limit of infinite acceleration, the entanglement in a fermionic-field bipartite system must be independent of the choice of Unruh modes. This implies that most tensor product structures used previously to compute field entanglement in relativistic quantum information cannot give rise to physical results.
We introduce an arbitrary number of accessible modes when analyzing bipartite entanglement degradation due to Unruh effect between two partners Alice and Rob. Under the single mode approximation (SMA) a fermion field only had a few accessible levels due to Pauli exclusion principle conversely to bosonic fields which had an infinite number of excitable levels. This was argued to justify entanglement survival in the fermionic case in the SMA infinite acceleration limit. Here we relax SMA. Hence, an infinite number of modes are excited as the observer Rob accelerates, even for a fermion field. We will prove that, despite this analogy with the bosonic case, entanglement loss is limited. We will show that this comes from fermionic statistics through the characteristic structure it imposes on the infinite dimensional density matrix for Rob. Surprisingly, the surviving entanglement is independent of the specific maximally entangled state chosen, the kind of fermionic field analyzed, and the number of accessible modes considered. We shall discuss whether this surviving entanglement goes beyond the purely statistical correlations, giving insight concerning the black hole information paradox.
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.
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.
A uniformly accelerated observer perceives the Minkowski vacuum as a thermal bath, so acceleration acts as a noise channel on correlations shared with an inertial partner. For a Dirac field in the standard treatment, the resulting map is a one-sided amplitude-damping channel, and entanglement and quantum discord survive at infinite acceleration. We introduce a symmetric Unruh-like map in which the vacuum and the one-particle state both exchange amplitude with the inaccessible Rindler region; for a Bell state it yields a bit-flip channel whose flip probability is the Fermi-Dirac occupation at the Unruh temperature. Using negativity, mutual information, and all six pairwise quantum discords, we find that the entanglement and discord between the inertial observer and the accessible mode vanish together at infinite acceleration, leaving only one bit of classical correlation. These results show that the fate of quantum correlations in noninertial frames depends on the structure of the Minkowski-Rindler map.
We analyze the entanglement between two modes of a free Dirac field as seen by two relatively accelerated parties. The entanglement is degraded by the Unruh effect and asymptotically reaches a nonvanishing minimum value in the infinite acceleration limit. This means that the state always remains entangled to a degree and can be used in quantum information tasks, such as teleportation, between parties in relative uniform acceleration. We analyze our results from the point of view afforded by the phenomenon of entanglement sharing and in terms of recent results in the area of multiqubit complementarity.
We investigate the relativistic dynamics of quantum entanglement in a four-qubit cluster (CL4CL_4CL4​) state using a fully operational Unruh-DeWitt detector framework. Contrary to the widely held expectation that the Unruh effect inevitably degrades initially maximal entanglement, we demonstrate that the 1−31-31−3 bipartite entanglement of the CL4CL_4CL4​ state remains strictly maximal for all accelerations, including the infinite-acceleration limit. This result uncovers a previously unexplored phenomenon, namely the ``complete freezing of initially maximal entanglement" under relativistic motion. To the best of our knowledge, this is the first identification and systematic characterization of such a phenomenon within a relativistic framework. These findings overturn the conventional view that acceleration universally diminishes maximal entanglement and establish the CL4CL_4CL4​ state as a promising resource for quantum information processing in non-inertial or curved-spacetime settings.