The uncertainty principle is a striking and fundamental feature in quantum mechanics, distinguishing it from classical mechanics. It offers an important lower bound to predict outcomes of two arbitrary incompatible observables measured on a particle. In quantum information theory, this uncertainty principle is popularly formulized in terms of entropy. Here, we present an improvement of the tripartite quantum-memory-assisted entropic uncertainty relation. The uncertainty's lower bound is derived by considering mutual information and the Holevo quantity. It shows that the bound derived by this method will be tighter than the lower bound of Renes and Boileau [ Phys. Rev. Lett. 103, 020402 (2009)]. Furthermore, regarding a pair of mutual unbiased bases as the incompatibility, our bound will become extremely tight for the three-qubit $X$-state system, completely coinciding with the entropy-based uncertainty, and can restore Renes and Boileau's bound with respect to arbitrary tripartite pure states. In addition, by applying our lower bound one can attain the tighter bound of the quantum secret key rate, which is of basic importance to enhance the security of quantum key distribution protocols.

Neutrino oscillation is an important physical phenomenon in elementary particle physics, and its nonclassical features can be revealed by the Leggett–Garg inequality. It shows that its quantum coherence can be sustained over astrophysical length scales. In this work, we investigate the measure of quantumness in experimentally observed neutrino oscillations via the nonlocal advantage of quantum coherence (NAQC), quantum steering, and Bell nonlocality. From various neutrino sources, ensembles of reactor and accelerator neutrinos are analyzed at distinct energies, such as Daya Bay (0.5 km and 1.6 km) and MINOS (735 km) collaborations. The NAQC of two-flavor neutrino oscillation is characterized experimentally compared to the theoretical prediction. It exhibits non-monotonously evolutive phenomenon with the increase of energy. Furthermore, it is found that the NAQC is a stronger quantum correlation than quantum steering and Bell nonlocality even in the order of km. Hence, for an arbitrary bipartite neutrino-flavor state with achieving a NAQC, it must be also a steerable and Bell nonlocal state. The results might offer an insight into the neutrino oscillation for the further applications on quantum information processing.

Recently, an entropic uncertainty relation for multiple measurements was proposed by Liu et al. [ Phys. Rev. A 91, 042133 (2015)]. However, the lower bound of the relation is not always tight with respect to different measurements. Herein, we improve the lower bound of the entropic uncertainty relation for multiple measurements, referred to as a simply constructed bound (SCB). We verify that the SCB is tighter than Liu et al.'s result for arbitrary mutually unbiased basis measurements, which might play a fundamental and crucial role in practical quantum information processing. Moreover, we optimize the SCB by considering mutual information and the Holevo quantity, and propose an optimized SCB. Notably, the proposed bounds are extrapolations of the behavior of two measurements to a larger collection of measurements. It is believed that our findings would shed light on entropy-based uncertainty relations in the multiple measurement scenario and will be beneficial for security analysis in quantum key distributions.

We explore the tripartite entropic uncertainty and genuine tripartite quantumness of Dirac fields in the background of the Garfinkle–Horowitz–Strominger (GHS) dilation space-time. It is interesting to note that Hawking radiation leads to the decay of quantum nonlocality in the physically accessible region while preserving its total coherence. More importantly, it demonstrates an intrinsic trade-off relationship between the coherences of physically accessible and inaccessible regions. Moreover, we examine the effect of Hawking radiation on entropy-based measured uncertainty and find that stronger Hawking radiation causes the uncertainty in physically accessible regions to increase while decreasing the uncertainty in physically inaccessible regions. Therefore, our investigations may be beneficial to a better understanding of the system’s quantumness in a curved space-time. Combining relativity theory with quantum information science offers new avenues for comprehending the information paradoxes involving black holes.

We studied the dynamics of entropic uncertainty in Markovian and non-Markovian systems during the charging of open quantum batteries (QBs) mediated by a common dissipation environment. In the non-Markovian regime, the battery is almost fully charged efficiently, and the strong non-Markovian property is beneficial for improving the charging power. In addition, the results show that the energy storage is closely related to the couplings of the charger-reservoir and battery-reservoir; that is, the stronger coupling of a charger reservoir improves energy storage. In particular, entanglement is required to obtain the most stored energy and is accompanied by the least tight entropic bound. Interestingly, it was found that the tightness of the entropic bound can be considered as a good indicator of the energy transfer in different charging processes, and the complete energy transfer always corresponds to the tightest entropic bound. Our results provide insight into the optimal charging efficiency of QBs during practical charging.