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arXiv:1511.03029 · The European Physical Journal C

Quantum Fisher and skew information for Unruh accelerated Dirac qubit

Subhashish Banerjee, Ashutosh Kumar Alok, S. Omkar

Published Aug 1, 2016• 15 citations
arXivHTMLPDF

Abstract

We develop a Bloch vector representation of the Unruh channel for a Dirac field mode. This is used to provide a unified, analytical treatment of quantum Fisher and skew information for a qubit subjected to the Unruh channel, both in its pure form as well as in the presence of experimentally relevant external noise channels. The time evolution of Fisher and skew information is studied along with the impact of external environment parameters such as temperature and squeezing. The external noises are modelled by both purely dephasing phase damping and the squeezed generalised amplitude damping channels. An interesting interplay between the external reservoir temperature and squeezing on the Fisher and skew information is observed, in particular, for the action of the squeezed generalised amplitude damping channel. It is seen that for some regimes, squeezing can enhance the quantum information against the deteriorating influence of the ambient environment. Similar features are also observed for the analogous study of skew information, highlighting a similar origin of the Fisher and skew information.

DOI
10.1140/epjc/s10052-016-4290-7

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We develop a Bloch vector representation of the Unruh channel for a Dirac field mode. This is used to provide a unified, analytical treatment of quantum Fisher and skew information for a qubit subjected to the Unruh channel, both in its pure form as well as in the presence of experimentally relevant external noise channels. The time evolution of Fisher and skew information is studied along with the impact of external environment parameters such as temperature and squeezing. The external noises are modelled by both purely dephasing phase damping and the squeezed generalised amplitude damping channels. An interesting interplay between the external reservoir temperature and squeezing on the Fisher and skew information is observed, in particular, for the action of the squeezed generalised amplitude damping channel. It is seen that for some regimes, squeezing can enhance the quantum information against the deteriorating influence of the ambient environment. Similar features are also observed for the analogous study of skew information, highlighting a similar origin of the Fisher and skew information.
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.
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.
Abstract The inherent association between real quantum systems and their surrounding environment invariably results in decoherence, leading to the loss of entanglement. This diminution in entanglement coincides with a decline in the fidelity of transmitted information using the entangled quantum resource. This study scrutinizes the impact of the squeezed generalized amplitude damping (SGAD) channel on quantum Fisher information (QFI) parameters. The SGAD channel model, a versatile framework, is also employed to simulate other dissipative channels, including amplitude damping (AD) and generalized amplitude damping (GAD). Kraus operators facilitate the modeling of noisy channels. The results reveal that, within the SGAD channel, the QFI remains impervious to the squeezing variables (r and Φ\PhiΦ Φ ). In the GAD channel, FθGADF\theta _{GAD}FθGAD​ F θ GAD undergoes enhancement to a constant value with an upswing in temperature (T), while the ϕ\phiϕ ϕ parameter in the GAD channel, FϕGADF\phi _{GAD}FϕGAD​ F ϕ GAD , akin to the SGAD channel, surges around T = 2 before complete loss ensues. Concerning the AD channel, the θ\thetaθ θ component of the QFI initially experiences decoherence with an augmentation in the AD noise parameter ( λ\lambdaλ λ ). Subsequently, it is restored to its initial value with a further escalation in λ\lambdaλ λ . Conversely, the ϕ\phiϕ ϕ component of the QFI in the AD channel experiences decoherence with an elevation in the AD noise parameter ( λ\lambdaλ λ ).
We give the explicit expressions of quantum Fisher information and skew information for a two-qubit Bell states. We investigate their dynamics under the decoherence effects: phase-damping channel, depolarizing channel and amplitude-damping channel. We also discuss the thermal entanglement quantified by Wootters concurrence for these three decoherence channels and we compare its dynamical behavior with the quantum Fisher information and skew information. We then use this comparison to investigate the influence of noisy channels on thermal entanglement and its role in boosting the performance of metrology protocols. It is shown that the correlations in two-qubit Bell states are more resistant to phase-damping channel and depolarizing channels.
We investigate the performance of quantum Fisher information (QFI) under the Unruh-Hawking effect, where one of the observers (e.g., Rob) is uniformly accelerated with respect to other partners. In the context of relativistic quantum information theory, we demonstrate that quantum Fisher information, as an important measure of the information content of quantum states, has a rich and subtle physical structure compared with entanglement or Bell nonlocality. In this work, we mainly focus on the parametrized (and arbitrary) pure two-qubit states, where the weight parameter $\ensuremath{\theta}$ and phase parameter $\ensuremath{\phi}$ are naturally introduced. Intriguingly, we prove that QFI with respect to $\ensuremath{\theta}$ (${\mathcal{F}}_{\ensuremath{\theta}}$) remains unchanged for both scalar and Dirac fields. Meanwhile, we observe that QFI with respect to $\ensuremath{\phi}$ (${\mathcal{F}}_{\ensuremath{\phi}}$) decreases with the increase of acceleration rrr but remains finite in the limit of infinite acceleration. More importantly, our results show that the symmetry of ${\mathcal{F}}_{\ensuremath{\phi}}$ (with respect to $\ensuremath{\theta}=\ensuremath{\pi}/4$) has been broken by the influence of the Unruh effect for both cases.
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.