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Quantum Information Processing

Exploration of entropic uncertainty relation for two accelerating atoms immersed in a bath of electromagnetic field

Zhiming Huang, Haozhen Situ

Published Dec 13, 2018• 11 citations
Publisher
DOI
10.1007/s11128-018-2151-z

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Quantum uncertainty is deeply linked to quantum correlations and relativistic motion. The entropic uncertainty relation with quantum memory offers a powerful way to study how shared entanglement affects measurement precision. However, under acceleration, the Unruh effect can degrade quantum correlations, raising questions about the reliability of QMA-EUR in such settings. Here, we investigate the QMA-EUR for two uniformly accelerating Unruh-DeWitt detectors coupled to a massless scalar field. Using the Kossakowski-Lindblad master equation, we calculate the entropic uncertainty, its lower bound, and the tightness of the relation under different Unruh temperatures. We find that acceleration does not always increase the lower bound on the uncertainty relation. Depending on the initial correlations between the detectors, it may either increase or decrease. This behavior results from the interplay between quantum discord and minimal missing information. Interestingly, a higher quantum discord does not necessarily lead to lower uncertainty.

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Quantum-memory-assisted entropic uncertainty in fluctuating electromagnetic field with a boundary

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In this work, we investigate the dynamics of quantum-memory-assisted entropic uncertainty relation for a two-level atom coupled with fluctuating electromagnetic field in the presence of a perfectly reflecting plane boundary. The solution of the master equation that governs the system evolution is derived. We find that entropic uncertainty and mixedness increase to a stable value with evolution time, but quantum correlation reduces to zero with evolution time. That is, the mixedness is positively associated with entropic uncertainty, however, increasing quantum correlation can cause the decrease of the uncertainty. The tightness of entropic uncertainty grows at first and then declines to zero with evolution time. In addition, entropic uncertainty fluctuates to relatively stable values with increasing the atom’s distance from the boundary, especially for short evolution time, which suggests a possible way of testing the vacuum fluctuating and boundary effect. Finally, we propose an effective method to control the uncertainty via quantum weak measurement reversal.

Modern Physics Letters A•Mar 26, 2019•2 citations
Quantum uncertainty is deeply linked to quantum correlations and relativistic motion. The entropic uncertainty relation with quantum memory offers a powerful way to study how shared entanglement affects measurement precision. However, under acceleration, the Unruh effect can degrade quantum correlations, raising questions about the reliability of QMA-EUR in such settings. Here, we investigate the QMA-EUR for two uniformly accelerating Unruh-DeWitt detectors coupled to a massless scalar field. Using the Kossakowski-Lindblad master equation, we calculate the entropic uncertainty, its lower bound, and the tightness of the relation under different Unruh temperatures. We find that acceleration does not always increase the lower bound on the uncertainty relation. Depending on the initial correlations between the detectors, it may either increase or decrease. This behavior results from the interplay between quantum discord and minimal missing information. Interestingly, a higher quantum discord does not necessarily lead to lower uncertainty.
In this work, we investigate the dynamics of quantum-memory-assisted entropic uncertainty relation for a two-level atom coupled with fluctuating electromagnetic field in the presence of a perfectly reflecting plane boundary. The solution of the master equation that governs the system evolution is derived. We find that entropic uncertainty and mixedness increase to a stable value with evolution time, but quantum correlation reduces to zero with evolution time. That is, the mixedness is positively associated with entropic uncertainty, however, increasing quantum correlation can cause the decrease of the uncertainty. The tightness of entropic uncertainty grows at first and then declines to zero with evolution time. In addition, entropic uncertainty fluctuates to relatively stable values with increasing the atom’s distance from the boundary, especially for short evolution time, which suggests a possible way of testing the vacuum fluctuating and boundary effect. Finally, we propose an effective method to control the uncertainty via quantum weak measurement reversal.