Tighter Bound of Entropic Uncertainty under the Unruh Effect

Abstract

The uncertainty principle limits the ability to simultaneously predict measurement outcomes for two non‐commuting observables of a quantum particle. However, the uncertainty can be violated by considering a particle as a quantum memory correlated with the primary particle. By modeling an Unruh–Dewitt detector coupled to a massless scalar field, it is explored how the Unruh effect affects the entropic uncertainty and the tighter lower bound for a pair of entangled detectors is probed when one of them is accelerated. It is found that Unruh thermal noise really gives rise to an increase of entropic uncertainty for the given conditions since the correlation between quantum memory and the measured system is decreased. It is shown that the bound of the entropic uncertainty relations, in the presence of memory, can be formulated by introducing the Holevo quantity and mutual information. It is also noticed that Adabi's lower bound is tighter than that of Berta, and just the optimal bound under the Unruh effect. Moreover, it is shown that Berta's lower bound is unrelated to the choice of complementary observables, while the optimal Adabi's lower bound is dependent on the measurement choice. It is worth mentioning that the investigations may offer a better understanding of the entropic uncertainty in a relativistic motion.

Quantum correlations and coherence in a moving Unruh–deWitt detector

“…Recently, different approaches have been employed to study the quantum effects like entanglement, quantum correlations and coherence [29][30][31][32][33][34]. Moreover, the quantum correlation and entropic uncertainty relation are also investigated in a multipartite scenario [35,36].…”

Tripartite entropic uncertainty relation under phase decoherence

“…These new formulations of the uncertainty principle have facilitated the emergence of many potential applications in the field of quantum information, including cryptography 9 , 10 , quantum metrology 11 , 12 , quantum randomness 13 , 14 and entanglement witness 15 – 18 . Much interest has been focused on clarifying how the QMA-EUR evolves in various systems including Heisenberg spin models 19 – 28 , Unruh–DeWitt detector model 29 , 30 , neutrino oscillations 31 and some open quantum systems 21 , 31 – 35 .…”