Abstract In this paper, we analytically explore the effect of Hawking radiation on quantum Fisher information (QFI) for Dirac particles in the background of Schwarzschild black hole. What surprise us is that the Hawking radiation could not disturb QFI with respect to the state parameter ( ). Additionally, we also find in the case of an almost extreme black hole, or when the black hole is approximate to evaporating completely, QFI with respect to the Hawking temperature T ( ) always being zero indicates that the parameter estimation precision about the Hawking temperature is minimum in the two situations above. In particular, the maximal is obtained when the Hawking temperature is a fixed value for every state parameter . Furthermore, we investigate how the Hawking effect influences the distribution of the QFI over subsystems in physical accessible regions and find that QFI can be either subadditive or superadditive, depending on the specific parameter under the Hawking effect. At last, we also study the QFI of other possible bipartite divisions, which are physically inaccessible, and the nontrivial results reveal that QFI is averagely distributed in different physical regions.
Previous studies have shown that the decoherence of environments generally negatively influences the quantum correlations in the Schwarzschild black hole . In our paper, we find that the decoherence of the generalized amplitude damping (GAD) channel has both positive and negative effects on the quantum coherence of Dirac fields, which means that the decoherence of environments can not only reduce the quantum coherence but also increase the quantum coherence in Schwarzschild spacetime. This result banishes the widespread belief that the decoherence of the environment can only destroy the quantum coherence in curved spacetime. Furthermore, another novel phenomenon has been observed for the first time: with increasing Hawking temperature T, the QFI of physically inaccessible modes rapidly decays from infinity to 0, which may provide a way to detect whether the particles enter the physically inaccessible region or not. This result may provide a new perspective for exploring and analyzing black holes.
We explore the performance of various correlation measures for open Dirac system with Hawking effect in Schwarzschild space–time. Our results indicate that the impact of Hawking effect on physical accessible entanglement is weaker than that of decoherence. For generalized amplitude damping (GAD) channel, the entanglement sudden death (ESD) is analyzed in detail, and the inequivalence of quantization for Dirac particles in the black hole and Kruskal space–time is verified via quantum discord measure. In addition, as an example for interpreting Bell non-locality, we study the GAD channel with Hawking effect. It can be noticed that there is a boundary line of Bell violation for physically accessible states. That is, quantum non-locality would disappear when Hawking temperature exceeds a certain value. This critical temperature increases as a decoherence parameter decreases. In the case of phase damping (PD) channel, the interaction between the particle and noise environment does not produce bipartite system–environment entanglement. Then we discuss entanglement distributions, and find that the reduced physically accessible entanglement can be redistributed to physical inaccessible region. At last, we extend our investigation to an N-qubit system, and obtain a universal expression of the physical accessible entanglement.
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 Φ ). In the GAD channel,
FθGAD F θ GAD undergoes enhancement to a constant value with an upswing in temperature (T), while the
ϕ ϕ parameter in the GAD channel,
FϕGAD F ϕ GAD , akin to the SGAD channel, surges around T = 2 before complete loss ensues. Concerning the AD channel, the
θ θ component of the QFI initially experiences decoherence with an augmentation in the AD noise parameter (
λ λ ). Subsequently, it is restored to its initial value with a further escalation in
λ λ . Conversely, the
ϕ ϕ component of the QFI in the AD channel experiences decoherence with an elevation in the AD noise parameter (
λ λ ).
Abstract We introduce and study a quantum channel that arises from the structure of the vacuum state of Dirac fields propagating in a Garfinkle–Horowitz–Strominger (
GHS GHS ) dilation black hole spacetime. We put forward the concept of quantum information divergence, which is a new measure for relativistic parameter estimation. We employ quantum metrology to estimate the amplitude and relative phase of a Dirac field state using the quantum Fisher information and information divergence. The decoherence of quantum parameter estimation is studied through the evolution of the Bloch vector for arbitrary initial states subjected to the quantum channel and external noises. We find that the quantum information divergence decreases more than the quantum Fisher information as a function of the radiation temperature. Due to the Pauli exclusion principle and Dirac statistics, the estimation precision will gradually decrease to a non-zero value. In order to study the decoherence in the dilation black hole, we obtain the monotonic decrease of quantum coherence when an initial field evolves from the highly correlated state to the current cosmic background. The external noises can further suppress the decoherence effect from the black hole.
Abstract In this letter, we mainly investigate how to enhance the damaged quantum entanglement under an open Dirac system with the Hawking effect within Schwarzschild space-time. We consider that particle A held by Alice undergoes generalized amplitude damping noise in a flat space-time, and that another particle B by Bob entangled with A is under a Schwarzschild space-time. Subsequently, we put forward a physical scheme to recover the damaged quantum entanglement by prior weak measurement on subsystem A before the interaction with the decoherence noise followed by post-measurement filtering operation. The results indicate that our scheme can effectively recover the damaged quantum entanglement affected by the Hawking effect and the noisy channel. Thus, our work might be beneficial to understand the dynamic behavior of the quantum state and recover the damaged quantum entanglement with open Dirac systems under the Hawking effect in the background of a Schwarzschild black hole.