Entropic uncertainty relation for qubits

Zuo-Yuan Zhang, Jinming Liu

Iwo Białynicki‐Birula, Łukasz Rudnicki

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.

Iwo Białynicki‐Birula

Xue‐Min Bai, Naitao Xue, Ni Liu +2 more

Abstract Based on a simple cavity‐engineered architecture, the dynamics of quantum memory–assisted entropic uncertainty relation (QMA‐EUR) for two qubits initially prepared in a generic Werner state is investigated. The effects of cavity decay rate, qubit–cavity couplings, and cavity–cavity couplings on the uncertainty are explored. It is found that the damped oscillation of uncertainty can be induced by the increase of two types of coupling strengths mentioned above. It is demonstrated that the maximum value of uncertainty is closely related to the purity of the initial state. The uncertainty can be either increased or decreased, depending on the threshold value of coupling strength between the two cavities. Finally, in agreement with a recent observation, an asynchronous relation between uncertainty and mixedness is found during the initial time evolution.