Complexity and entropic uncertainty of quantum systems

Meng-Long Song, Xue‐Ke Song, Ye Liu +1 more

In this study, we investigate the effectiveness of entropic uncertainty relations (EURs) in discerning the energy variation in quantum batteries (QBs) modelled by battery-charger field in the presence of bosonic and fermionic reservoirs. Our results suggest that the extractable works (exergy and ergotropy) have versatile characteristics in different scenarios, resulting in a complex relationship between tightness and extractable work. It is worth noting that the tightness of the lower bound of entropic uncertainty can be a good indicator for energy conversion efficiency in charging QBs. Furthermore, we disclose how the EUR including uncertainty and lower bound contributes to energy conversion efficiency in the QB system. It is believed that these findings will be beneficial for better understanding the role of quantum uncertainty in evaluating quantum battery performance.

Iwo Białynicki‐Birula, Łukasz Rudnicki

Yanliang Zhang, Mao-Fa Fang, Guodong Kang +1 more

We have investigated the dynamic features of the quantum-memory-assisted entropic uncertainty relation (QMA EUR) in the amplitude damping (AD) channel. The initial state of qubit system and quantum memory system shared between Alice and Bob is assumed as extended by Werner-like (EWL) state. To reduce the amount of entropic uncertainty of Pauli observables in this noisy channel, we presented a reduction scheme by means of weak measurements (WMs) and weak measurement reversals (WMRs) before and after the entangled system subjecting to the noisy channel. It is shown that the prior WM and poster WMR can effectively reduce quantity of entropic uncertainty, but the poster WM operation cannot played a positive role on reduction of quantity of entropic uncertainty. We hope that our proposal could be verified experimentally and might possibly have future applications in quantum information processing.

Iwo Białynicki‐Birula

Göktuğ Karpat

Entropic uncertainty relations quantify the limits on the predictability of quantum measurements. When the measured system is correlated with a quantum memory, these limits are described by the memory-assisted entropic uncertainty relation (MA-EUR). We examine the behavior of MA-EUR when the memory qubit undergoes noisy dynamics implemented via high-order controlled processes, namely, the quantum switch and the quantum time-flip. We consider a setting in which the control qubit is the very system on which the measurements are performed, while the target qubit serves as a noisy quantum memory. Focusing on Pauli channels, we show that feeding them into the quantum switch and the quantum time-flip can significantly reduce the total entropic uncertainty as compared to their direct application. Our results reveal that indefinite causal order and input-output direction can serve as resources to mitigate the effects of noise in the context of MA-EUR and its applications.

Feng-He Ju, Zuo-Yuan Zhang, Jin‐Ming Liu

Abstract We investigate the quantum-memory-assisted entropic uncertainty relation (QMA-EUR) in a Heisenberg XYZ mixed-spin (1/2, 1) model. Coupling strength, Dzyaloshinskii–Moriya (DM) interaction and inhomogeneous magnetic field, respectively, contributing to QMA-EUR by a thermal entanglement in the hybrid-spin model are studied in detail. Furthermore, we compare the uncertainty of the bipartite hybrid model with those of qubit–qubit and qutrit–qutrit systems. Meanwhile, the effects of local PT-symmetric operation and weak measurement on the steering of entropic uncertainty are analyzed. We find that the local PT-symmetric operation can reduce the entropic uncertainty, and the entropic uncertainty can also be decreased by weak measurement reversal.