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Communications in Theoretical Physics

Quantum Fisher information of a qubit-qutrit system in Garfinkle–Horowitz–Strominger dilation space–time

Yi-Jun Lian, Jin‐Ming Liu

Published May 17, 2021• 24 citations
Publisher

Abstract

Abstract We investigate the quantum Fisher information (QFI) of a qubit-qutrit system in the background of Garfinkle–Horowitz–Strominger dilation black hole. After deriving the analytical expression of the QFI, we examine its dynamics with respect to the dilation parameter D and the state parameter γ of the system. Our results show that the QFI for the estimation of γ is a fixed value, which is independent of the parameters D and γ . And the QFI for the estimation of D varies with the parameters D and γ . Additionally, we propose an effective strategy to steer the QFI by introducing weak measurement reversal. We find that the QFI can be remarkably enhanced by adjusting the appropriate reversing measurement strengths. Our findings might provide some useful insights for the study on parameter estimation of hybrid systems in the framework of relativity theory.

DOI
10.1088/1572-9494/ac01e4

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Abstract We investigate the quantum Fisher information (QFI) of a qubit-qutrit system in the background of Garfinkle–Horowitz–Strominger dilation black hole. After deriving the analytical expression of the QFI, we examine its dynamics with respect to the dilation parameter D and the state parameter γ of the system. Our results show that the QFI for the estimation of γ is a fixed value, which is independent of the parameters D and γ . And the QFI for the estimation of D varies with the parameters D and γ . Additionally, we propose an effective strategy to steer the QFI by introducing weak measurement reversal. We find that the QFI can be remarkably enhanced by adjusting the appropriate reversing measurement strengths. Our findings might provide some useful insights for the study on parameter estimation of hybrid systems in the framework of relativity theory.
Abstract The quantum‐memory‐assisted entropic uncertainty relation for Dirac particles in the background of a Garfinkle–Horowitz–Strominger (GHS) dilation black hole is investigated, and the relationship between the entropy uncertainty and the quantum entanglement of a hybrid qubit–qutrit state in the GHS space–time analyzed. The results show that the physically accessible uncertainty increases while the inaccessible uncertainty decreases as the dilation parameter of the black hole enhances. Moreover, the evolution behavior of the uncertainty is inversely correlated with that of the entanglement between the quantum memory and the particle to be measured. Meanwhile, a method to steer the entropic uncertainty with the technique of weak measurement reversal is proposed. It is found that the uncertainty can be reduced effectively by adjusting the appropriate measurement strength. These findings may lead to a deeper understanding of entropy uncertainty dynamics, as well as its steering in a curved space–time.
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\mathrm {GHS}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 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.
Quantum Fisher Information (QFI) is a fundamental quantity in quantum parameter estimation theory, characterizing the ultimate precision bound of parameter estimation. In this work, we investigate QFI for quantum states in non-Hermitian systems. By employing the projected Hilbert space method and spectral decomposition, we derive an explicit expression for the QFI in terms of the density matrix and parameter generators. This formulation not only recovers the well-known results in the Hermitian case but also captures the non-Hermitian effects induced by the time-dependent norm of the state. To validate our theoretical framework, we analyze a single-qubit pseudo-Hermitian system and apply Naimark dilation theory to embed it into an equivalent Hermitian system. The comparison between the original and dilated systems demonstrates the consistency and applicability of the proposed QFI formula in non-Hermitian settings. In addition, we investigate a PT\mathcal{PT}PT-symmetric system to further explore the influence of non-Hermiticity on QFI. Our findings offer a new perspective for analyzing and enhancing QFI in non-Hermitian systems, paving the way for promising applications in non-Hermitian quantum metrology and sensing.
Quantum Fisher information (QFI) quantifies the sensitivity of a quantum state to a parameter change and plays a key role in quantum metrology. Meanwhile, quantum coherence is a crucial resource for quantum information processing. However, despite extensive studies on various aspects of quantum metrology, the interplay between the dynamics of the QFI and quantum coherence remains unexplored. Here, we explore the factorization relationship between the QFI and quantum coherence, both theoretically and experimentally. We prepare pure states in qubit and qutrit systems and apply unitary evolution to investigate this relationship. Our results confirm the factorization law, offering strong evidence for this relationship. Furthermore, we establish a lower bound on the variance of the estimated parameter that does not require the final state information. This approach reveals a deep connection between the QFI and quantum coherence, providing insights into quantum parameter estimation. These findings have potential applications in quantum sensing and quantum metrology.
Abstract We explore the tripartite entropic uncertainty and genuine tripartite quantumness of Dirac fields in the background of the Garfinkle–Horowitz–Strominger (GHS) dilation space-time. It is interesting to note that Hawking radiation leads to the decay of quantum nonlocality in the physically accessible region while preserving its total coherence. More importantly, it demonstrates an intrinsic trade-off relationship between the coherences of physically accessible and inaccessible regions. Moreover, we examine the effect of Hawking radiation on entropy-based measured uncertainty and find that stronger Hawking radiation causes the uncertainty in physically accessible regions to increase while decreasing the uncertainty in physically inaccessible regions. Therefore, our investigations may be beneficial to a better understanding of the system’s quantumness in a curved space-time. Combining relativity theory with quantum information science offers new avenues for comprehending the information paradoxes involving black holes.