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Classical and Quantum Gravity

Quantum correlation affected by quantum gravitational fluctuation

Zhiming Huang

Published Jul 1, 2019• 3 citations
Publisher

Abstract

Abstract We study the behaviors of quantum correlation for two independent gravitationally polarizable subsystems interacting with fluctuating quantum gravitational field. We firstly derive the master equation that the system evolution obeys. Then we discuss the generation, revival, attenuation and enhancement of quantum correlation, which are dependent on the initial state, separation and polarization of the two subsystems. It is shown that quantum correlation for correlated initial state can be preserved effectively from the quantum gravitational fluctuation when the separation between the two subsystems is sufficiently small. Compared with the entanglement behaviors, it is shown that quantum correlation presents better robustness than entanglement, which may be helpful to quantum information processing. Furthermore, the initial state, separation and polarization of the subsystems give us more freedom to manipulate the behaviors of quantum correlation under quantum gravitational decoherence. Our study would throw light on our exploration of quantum gravity.

DOI
10.1088/1361-6382/ab2e41

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Abstract We study the behaviors of quantum correlation for two independent gravitationally polarizable subsystems interacting with fluctuating quantum gravitational field. We firstly derive the master equation that the system evolution obeys. Then we discuss the generation, revival, attenuation and enhancement of quantum correlation, which are dependent on the initial state, separation and polarization of the two subsystems. It is shown that quantum correlation for correlated initial state can be preserved effectively from the quantum gravitational fluctuation when the separation between the two subsystems is sufficiently small. Compared with the entanglement behaviors, it is shown that quantum correlation presents better robustness than entanglement, which may be helpful to quantum information processing. Furthermore, the initial state, separation and polarization of the subsystems give us more freedom to manipulate the behaviors of quantum correlation under quantum gravitational decoherence. Our study would throw light on our exploration of quantum gravity.
In this article, we investigate the dynamics of quantum correlation for two atoms interacting with massless scalar field in the background of de Sitter spacetime. We firstly derive the solving process of master equation that governs the system evolution with initial Werner state. Then we discuss the production, revival and decay of quantum correlation for three cases of different initial states: zero-correlation state, non zero-correlation separable state and maximally entangled state. We find that quantum correlation degrades as temperature and the two-atom distance increase. Compared with the sudden death and birth of entanglement, quantum correlation change more smoothly and thus is more robust to decoherence, which can remain stable for long time when two atoms are very close.
A quantum master equation describing the stochastic dynamics of a quantum massive system interacting with a quantum gravitational field is useful for the investigation of quantum gravitational and quantum informational issues such as the quantum nature of gravity, gravity-induced entanglement and gravitational decoherence. Studies of the decoherence of quantum systems by an electromagnetic field shows that a lower temperature environment is more conducive to successful quantum information processing experiments. Likewise, the quantum nature of (perturbative) gravity is far better revealed at lower temperatures than high, minimizing the corruptive effects of thermal noise. In this work, generalizing earlier results of the Markovian ABH master equation [1,2] which is valid only for high temperatures, we derive a non-Markovian quantum master equation for the reduced density matrix, and the associated Fokker-Planck equation for the Wigner distribution function, for the stochastic dynamics of two masses following quantum trajectories, interacting with a graviton field, including the effects of graviton noise, valid for all temperatures. We follow the influence functional approach exemplified in the derivation of the non-Markovian Hu-Paz-Zhang master equation [62,64] for quantum Brownian motion. We find that in the low temperature limit, the off-diagonal elements of the reduced density matrix decrease in time logarithmically for the zero temperature part and quadratically in time for the temperature-dependent part, which is distinctly different from the Markovian case. We end with a summary of our findings and a discussion on how this problem studied here is related to the quantum stochastic equation derived in [77] for gravitational self force studies, and to quantum optomechanics where experimental observation of gravitational decoherence and entanglement may be implemented.
Abstract We address the time evolution of quantum correlations (QCs) such as entanglement, purity, and coherence for a model of two non-interacting qubits initially prepared as a maximally entangled bipartite state. We contrast the comparative potential of the classical fields to preserve these QCs in the noisy and noiseless realms. We also disclose the characteristic dynamical behavior of the QCs of the two-qubit state under the static noise effects originating from the common and different configuration models. We show that there is a direct connection between the fluctuations allowed by an environment and the preservation of QCs. Due to the static noise dephasing effects, the QCs are suppressed, resulting in the separability of the two-qubit entangled state after a finite duration. For bipartite QCs preservation, we show that the common configuration is more resourceful than the different configuration. Furthermore, this protection of the QCs under static noise for large intervals is entirely attributable to the existence of the entanglement sudden death and birth phenomenon. Most importantly, we found the bipartite QCs less fragile than the tripartite ones in comparison under the static noise. In addition, we find the concurrence measure to show more evident revivals of entanglement in comparison.
In this paper, we investigate the behaviors of quantum correlation quantified by trace norm measurement-induced nonlocality (TMIN) for two uniformly accelerated atoms coupled with electromagnetic vacuum fluctuation in the Minkowski vacuum. We firstly discuss the solving process of master equation that governs the system evolution based on the Pauli matrix presentation for two-qubit state. Similar to [Y. Q. Yang et al., Phys. Rev. A 94, 032337 (2016)], we analyze the degradation, creation, revival and enhancement of quantum correlation for different initial states and polarizations of two atoms, and the influence of interatomic separation and acceleration on quantum correlation. Compared with the entanglement dynamics discussed in [Y. Q. Yang et al., Phys. Rev. A 94, 032337 (2016)], it is found that quantum correlation exhibits better robustness than entanglement. This may be helpful for quantum information processing.
Abstract Schemes of gravitationally induced decoherence are being actively investigated as possible mechanisms for the quantum-to-classical transition. Here, we introduce a decoherence process due to quantum gravity effects. We assume a foamy quantum spacetime with a fluctuating minimal length coinciding on average with the Planck scale. Considering deformed canonical commutation relations with a fluctuating deformation parameter, we derive a Lindblad master equation that yields localization in energy space and decoherence times consistent with the currently available observational evidence. Compared to other schemes of gravitational decoherence, we find that the decoherence rate predicted by our model is extremal, being minimal in the deep quantum regime below the Planck scale and maximal in the mesoscopic regime beyond it. We discuss possible experimental tests of our model based on cavity optomechanics setups with ultracold massive molecular oscillators and we provide preliminary estimates on the values of the physical parameters needed for actual laboratory implementations.
A direct quantization of the Newtonian interaction between two masses is known to establish entanglement, which if detected would witness the quantum nature of the gravitational field. Gravitational interaction is yet compatible also with gravitational decoherence models relying on classical channels, hence unable to create entanglement. Here, we show in paradigmatic cases that, despite the absence of entanglement, a classical-channel model of gravity can still establish quantum correlations in the form of quantum discord between two masses. This is demonstrated for the Kafri-Taylor-Milburn (KTM) model and a recently proposed dissipative extension of this. In both cases, starting from an uncorrelated state, a significant amount of discord is generally created. This eventually decays in the KTM model, while it converges to a small stationary value in its dissipative extension. We also find that initial local squeezing on the state of the masses can significanlty enhance the generated discord.