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arXiv:2408.06869

Quantum obesity and steering ellipsoids for fermionic fields in dilaton black hole

Samira Elghaayda, Mahmoud Youssef Abd‐Rabbou, Mostafa Mansour

Published Aug 13, 2024• 0 citations
arXivHTMLPDF

Abstract

This paper investigates quantum obesity (QO), quantum discord (QD), and the quantum steering ellipsoid (QSE) for bipartite Gisin states subjected to Garfinkle-Horowitz-Strominger (GHS) dilation of spacetime on the second qubit. These three quantifiers are introduced to characterize quantum correlations beyond entanglement and can also function as entanglement witnesses. Our results demonstrate a monotonic decrease in the physical accessibility of both QD and QO as the dilation parameter increases within the region-I of the second qubit. Conversely, in the anti-particle region, the accessibility of QD and QO stabilizes at finite values of the dilation parameter owing to the influence of the Pauli exclusion principle and Fermi-Dirac statistics, subsequently increasing gradually. Notably, the QSE in the region-I expands as the Dirac field frequency rises and the dilation parameter diminishes, while the opposite trend is observed in the anti-particle region.

DOI
10.48550/arxiv.2408.06869

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This paper investigates quantum obesity (QO), quantum discord (QD), and the quantum steering ellipsoid (QSE) for bipartite Gisin states subjected to Garfinkle-Horowitz-Strominger (GHS) dilation of spacetime on the second qubit. These three quantifiers are introduced to characterize quantum correlations beyond entanglement and can also function as entanglement witnesses. Our results demonstrate a monotonic decrease in the physical accessibility of both QD and QO as the dilation parameter increases within the region-I of the second qubit. Conversely, in the anti-particle region, the accessibility of QD and QO stabilizes at finite values of the dilation parameter owing to the influence of the Pauli exclusion principle and Fermi-Dirac statistics, subsequently increasing gradually. Notably, the QSE in the region-I expands as the Dirac field frequency rises and the dilation parameter diminishes, while the opposite trend is observed in the anti-particle region.
Abstract This paper investigates quantum obesity, quantum discord, and the quantum steering ellipsoid (QSE) for bipartite Gisin states that are subjected to Garfinkle–Horowitz–Strominger (GHS) dilation of spacetime on the second qubit. These three quantifiers are introduced to characterize quantum correlations beyond entanglement and can also function as entanglement witnesses. A monotonic decrease in the physical accessibility of both quantum discord as demonstrate in the results and quantum obesity as the dilation parameter increases within the region‐I of the second qubit. Conversely, in the anti‐particle region, the accessibility of quantum discord and quantum obesity stabilizes at finite values of the dilation parameter owing to the influence of the Pauli exclusion principle and Fermi‐Dirac statistics, subsequently increasing gradually. Notably, the QSE in the region‐I expand as the Dirac field frequency rises and the dilation parameter diminishes, while the opposite trend is observed in the anti‐particle region.
Abstract Quantum obesity (QO) is a novel function introduced to quantify quantum correlations that go beyond traditional measures like entanglement, while also functioning as an entanglement witness. One of the key strengths of QO lies in its analyticity for arbitrary states of bipartite systems, making it a more accessible and versatile tool compared to other measures of quantum correlations, such as quantum discord. In this work, we highlight the importance of QO as a fundamental quantity for identifying signatures of quantum phase transitions, which are critical changes in the ground state of quantum systems driven by quantum fluctuations. We introduce a mechanism based on local filtering operations designed to enhance the critical behavior of QO near phase transition points, providing a deeper understanding of these phenomena. Furthermore, we present a theorem that characterizes how QO transforms under local quantum operations and classical communications (LOCC), which broadens its applicability to a wider range of quantum systems. This opens new avenues for exploring quantum criticality and other novel quantum phenomena by leveraging the analytically computable, pairwise QO, thus offering both theoretical insights and practical applications in quantum information science.
Abstract We study the dynamics of Gaussian quantum steering in the background of a Garfinkle–Horowitz–Strominger dilaton black hole. It is found that the gravity induced by dilaton field will destroy the quantum steerability between the inertial observer Alice and the observer Bob who hovers outside the event horizon, while it generates steering-type quantum correlations between the causally disconnected regions. Therefore, the observers can steer each other’s state by local measurements even though they are separated by the event horizon. Unlike quantum entanglement in the dilaton spacetime, the quantum steering experiences catastrophic behaviors such as “sudden death” and “sudden birth” with increasing dilaton charge. In addition, the dilaton gravity destroys the symmetry of Gaussian steering and the latter is always asymmetric in the dilation spacetime. Interestingly, the attainment of maximal steering asymmetry indicates the critical point between one-way and two-way steering for the two-mode Gaussian state in the dilaton spacetime.
ABSTRACT We investigate the influence of the Hawking effect on quantum entanglement by incorporating the spin degrees of freedom of Dirac fields in the background of a Garfinkle–Horowitz–Strominger (GHS) dilaton black hole. By analyzing the redistribution of correlations between causally accessible and inaccessible regions, we obtain analytical results showing that, as the dilaton increases, the physically accessible spin entanglement decreases monotonically while the inaccessible counterpart grows correspondingly, revealing a constrained transfer of quantum correlations across the event horizon rather than independent creation or destruction. From an information‐theoretic perspective, we demonstrate that the Hawking effect does not permit arbitrary redistribution of spin entanglement, but instead enforces a well‐defined monogamy relation that strictly governs how entanglement is shared among different bipartitions under gravitational evolution. These results indicate that the correlations initially shared by the observers are redistributed between accessible and inaccessible sectors through the Hawking‐induced Bogoliubov transformation, providing further insight into the structure of spin quantum correlations in curved spacetime and the role of horizon‐induced effects in reshaping quantum correlations. PACS numbers: 04.70.Dy, 03.65.Ud,04.62.+v
Abstract Quantum steering ellipsoid (QSE) can faithfully characterize arbitrary bipartite state, and provide a new method to visually investigate and capture various quantum nonlocalities. Note that the dissipation of quantum nonlocalities can be accelerated by the coupling between the system and the decoherence channel, which induces great challenges in detecting quantum nonlocalities. Herein, considering the scenario in which the subsystem of a two-qubit system is coupled with a decoherence channel, the quantum discord (QD) and concurrence are visually characterized and detected by employing the QSE. The results reveal that the QSE y and z semiaxes are responsible for the traits of the QD and concurrence under the bit flip channel. The x and y semiaxes dominate and visualize the QD and concurrence under the phase damping channel. Of particular note is that one can realize the detections of the QD and concurrence via the shape of the QSE. To be clearer, the disappearance of the QD can be ascertained according to a needle-shaped QSE or a vanishing QSE in the Bloch sphere. In contrast, one can witness the concurrence if the total semiaxis length is greater than one. Beyond this, our results visually reveal that quantum entanglement is a stronger quantum nonlocality than the QD from the perspective of geometry, and thus deepens the understanding of the quantum nonlocality.
Abstract We study the redistribution of the fermionic steering and the relation among fermionic Bell nonlocality, steering, and entanglement in the background of the Garfinkle–Horowitz–Strominger dilaton black hole. We analyze the meaning of the fermionic steering in terms of the Bell inequality in curved spacetime. We find that the fermionic steering, which is previously found to survive in the extreme dilaton black hole, cannot be considered to be nonlocal. We also find that the dilaton gravity can redistribute the fermionic steering, but cannot redistribute Bell nonlocality, which means that the physically inaccessible steering is also not nonlocal. Unlike the inaccessible entanglement, the inaccessible steering may increase non-monotonically with the dilaton. Furthermore, we obtain some monogamy relations between the fermionic steering and entanglement in dilaton spacetime. In addition, we show the difference between the fermionic and bosonic steering in curved spacetime.