Entropic uncertainty relations in Schwarzschild space-time

Abstract

The uncertainty principle is deemed as one of cornerstones in quantum mechanics, and exploring its lower limit of uncertainty will be helpful to understand the principle's nature. In this study, we propose a generalized entropic uncertainty relation for arbitrary multiple-observable in multipartite system, and further derive a tighter lower bound by considering Holevo quality and mutual information. Importantly, we detailedly discuss the proposed uncertainty relations and quantum coherence in the context of Schwarzschild space-time. It is interesting to find that Hawking radiation will damage the coherence of the physically accessible region and increase the uncertainty. Furthermore, we argue that the properties of the uncertainty in Schwarzschild space-time can be explained from the systems' purity and the information redistribution of the different regions. Therefore, it is believed that our findings provide the generalized entropic uncertainty relations in multipartite systems, which may facilitate us deeper understanding of quantumness and information paradox of the black holes.

8 pages, 6 figures, comments are welcome

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Cited by in corpus (15)

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• Nonseparability of multipartite systems in dilaton black hole
• Quantifying Quantumness in (A)dS spacetimes with Unruh-DeWitt Detector
• Entanglement and entropy uncertainty in black hole quantum atmosphere
• Quantum steering for different types of Bell-like states in gravitational background
• Multiqubit coherence of mixed states near event horizon
• Generalized entropic uncertainty relation and non-classicality in Schwarzschild black hole
• Entropic uncertainty and coherence in Einstein-Gauss-Bonnet gravity
• Do maximally entangled states always have an advantage over non-maximally entangled states in Schwarzschild black hole?
• Tighter entropic uncertainty relations in the presence of quantum memories for complete sets of mutually unbiased bases
• State-independent uncertainty relations on multipartite spin $1/2$-systems
• Non-monotonic evolution of multipartite entanglement under the Unruh effect
• Bosonic and fermionic mutual information of N-partite systems in dilaton black hole background
• Entropic uncertainty under indefinite causal order and input-output direction