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

References in corpus (8)

• Tunnelling, Temperature and Taub-NUT Black Holes
• Conjectured Strong Complementary Information Tradeoff
• Stronger uncertainty relations for the sum of variances
• Quantum discord and classical correlation can tighten the uncertainty principle in the presence of quantum memory
• Entropic uncertainty relations and locking: tight bounds for mutually unbiased bases
• Fine-grained lower limit of entropic uncertainty in the presence of quantum memory
• Majorization approach to entropic uncertainty relations for coarse-grained observables
• Uncertainty relation in Schwarzschild spacetime

Cited by in corpus (9)

• Gaussian tripartite steering in Schwarzschild black hole
• Entanglement and entropy uncertainty in black hole quantum atmosphere
• Generalized entropic uncertainty relation and non-classicality in Schwarzschild black hole
• Entropic uncertainty and coherence in Einstein-Gauss-Bonnet gravity
• Non-monotonic evolution of multipartite entanglement under the Unruh effect
• Bosonic and fermionic mutual information of N-partite systems in dilaton black hole background
• State-independent uncertainty relations on multipartite spin $1/2$-systems
• Entropic uncertainty under indefinite causal order and input-output direction
• Tighter entropic uncertainty relations in the presence of quantum memories for complete sets of mutually unbiased bases