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arXiv:1408.1477 · Quantum Information and Computation

The Unruh effect interpreted as a quantum noise channel

S. Omkar, R. Srikanth, Subhashish Banerjee, Ashutosh Kumar Alok

Published Jul 1, 2016• 14 citations
arXivHTMLPDF

Abstract

We make use of the tools of quantum information theory to shed light on the Unruh effect. A modal qubit appears as if subjected to quantum noise that degrades quantum information, as observed in the accelerated reference frame. The Unruh effect experienced by a mode of a free Dirac field, as seen by a relativistically accelerated observer, is treated as a noise channel, which we term the Unruh channel. We characterize this channel by providing its operator-sum representation, and study various facets of quantum correlations, such as, Bell inequality violations, entanglement, teleportation and measurement-induced decoherence under the effect. We compare and contrast this channel from conventional noise due to environmental decoherence. We show that the Unruh effect produces an amplitude-damping-like channel, associated with zero temperature, even though the Unruh effect is associated with a non-zero temperature. Asymptotically, the Bloch sphere subjected to the channel does not converge to a point, as would be expected by fluctuation-dissipation arguments, but contracts by a finite factor. We construct for the Unruh effect the inverse channel, a non-completely-positive map, that formally reverses the effect, and offer some physical interpretation.

DOI
10.26421/qic16.9-10-2

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We make use of the tools of quantum information theory to shed light on the Unruh effect. A modal qubit appears as if subjected to quantum noise that degrades quantum information, as observed in the accelerated reference frame. The Unruh effect experienced by a mode of a free Dirac field, as seen by a relativistically accelerated observer, is treated as a noise channel, which we term the Unruh channel. We characterize this channel by providing its operator-sum representation, and study various facets of quantum correlations, such as, Bell inequality violations, entanglement, teleportation and measurement-induced decoherence under the effect. We compare and contrast this channel from conventional noise due to environmental decoherence. We show that the Unruh effect produces an amplitude-damping-like channel, associated with zero temperature, even though the Unruh effect is associated with a non-zero temperature. Asymptotically, the Bloch sphere subjected to the channel does not converge to a point, as would be expected by fluctuation-dissipation arguments, but contracts by a finite factor. We construct for the Unruh effect the inverse channel, a non-completely-positive map, that formally reverses the effect, and offer some physical interpretation.
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.
In this work, we study an important facet of field theories in curved space-time, viz. the Unruh effect, by making use of ideas of statistical mechanics and quantum foundations. Aspects of decoherence and dissipation, natural artifacts of open quantum systems, along with foundational issues such as the trade-off between coherence and mixing as well as various aspects of quantum correlations are investigated in detail for the Unruh effect. We show how the Unruh effect can be quantified mathematically by the Choi matrix approach. We study how environmentally induced decoherence modifies the effect of the Unruh channel. The differing effects of a dissipative or non-dissipative environment are noted. Further, useful parameters characterizing channel performance such as gate and channel fidelity are applied here to the Unruh channel, both with and without external influences. Squeezing, which is known to play an important role in the context of particle creation, is shown to be a useful resource in a number of scenarios.
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 developed a Hermitian operator representation of the Unruh channel for a driven accelerated detector in the presence of external noise. This representation is then used to provide a generalized analytical approach to a non-inertial evolution subjected to quantum weak measurements. The quantum information facets were then improved by performing weak measurements before and after the quantum channel. The external noise was modeled using a phase damping channel. The prominent oscillations of the quantum information are caused by vacuum fluctuations of the quantum fields coupled to the detector. Steady values are obtained for the quantum coherence and quantum Fisher information using the Unruh effect. Thus, quantum weak measurements can effectively suppress the decoherence induced by the relativistic acceleration. By comparing with cases without weak measurements, we demonstrate that there exist some regions with optimal measurement strengths that enhance the quantum coherence and quantum Fisher information. The effects of conditional improvement on the quantum information facets are still obvious in the presence of external noise.
We investigate the effects of quantum decoherence generated by the Unruh effect in non-inertial frames under an amplitude damping channel and a phase damping channel, respectively, when the Unruh single particle has right and left components. We not only consider the influence of acceleration on entanglement, but also consider the influence of different rates between right and left components of the Unruh single-particle state on entanglement. We find that when the Unruh single-particle state has right and left components, i.e. |1⟩U = q L|0⟩I|1⟩II + q R|1⟩I|0⟩II, |q R|2 + |q L|2 = 1, with q L ≠ 0, there appears the sudden death of entanglement, which occurs earlier under both the amplitude damping channel and the phase damping channel with the increase of acceleration than that when the Unruh single-particle state only has a right component (q R = 1, q L = 0). We also find that the initial entanglement decreases with decrease of q R from 1 to 1/21/2.
The interaction of an accelerated observer with a quantum field can modify the entanglement and quantum information shared between observers, thereby affecting quantum communication in non-inertial frames. We formulate the standard teleportation protocol in a relativistic setting where Alice remains inertial while Rob undergoes uniform acceleration and is modeled as an Unruh-DeWitt detector locally coupled to a massive scalar field. The detector-field interaction initially leads to a loss of entanglement and quantum information shared between Alice and Rob. Remarkably, under acceleration, the anti-Unruh regime can reverse this degradation, leading to an increase in both the shared entanglement and the accessible quantum information. We further find that, in the anti-Unruh regime, the teleportation fidelity is independent of the local free-evolution time of Alice's and Rob's states. At high accelerations, the recovered entanglement and quantum information enhance the teleportation fidelity, which approaches unity under appropriate conditions. These results demonstrate that the anti-Unruh effect can protect and recover quantum entanglement and information in a non-inertial frame by reducing the detector's effective temperature and the associated decoherence.