Abstract:The uncertainty principle limits the ability to simultaneously predictmeasurement outcomes for two non-commuting observables of a quantumparticle. However, the uncertainty can be violated by considering a particle asa quantum memory correlated with the primary particle. By modeling anUnruh–Dewitt detector coupled to a massless scalar field, it is explored howthe Unruh effect affects the entropic uncertainty and the tighter lower boundfor a pair of entangled detectors is probed when one of them is accelerated. Itis found that Unruh thermal noise really gives rise to an increase of entropicuncertainty for the given conditions since the correlation between quantummemory and the measured system is decreased. It is shown that the bound ofthe entropic uncertainty relations, in the presence of memory, can beformulated by introducing the Holevo quantity and mutual information. It isalso noticed that Adabi’s lower bound is tighter than that of Berta, and justthe optimal bound under the Unruh effect. Moreover, it is shown that Berta’slower bound is unrelated to the choice of complementary observables, whilethe optimal Adabi’s lower bound is dependent on the measurement choice. Itis worth mentioning that the investigations may offer a better understandingof the entropic uncertainty in a relativistic motion.

https://doi.org/10.1002/andp.201900386