Zhang Yuxia, Tan Xiangguan, Qiu Tianhui
School of Science, Qingdao University of Technology, Qingdao, 266520, China.
College of Electronic and Information Engineering, Shandong University of Science and Technology, Qingdao, 266590, China.
Sci Rep. 2023 Aug 2;13(1):12530. doi: 10.1038/s41598-023-39612-6.
In this paper, we consider a qubit in four scenarios: with drive, without drive, and in the presence of dissipation and dephasing, to investigate the quantum violation of the Leggett-Garg inequality (LGI) in an energy constraint. In the case of the energy constraint, we find that under the coarsening measurement in reference and final resolution, the quantum violation of the LGI for the pure qubit is the most robust; on the other hand, the quantum violation of the LGI for the dephasing qubit is the most vulnerable, and the quantum violation of the LGI for driven qubit lies between that of pure qubit and dissipation qubit. Under the coarsening of measurement temporal reference, the quantum violation of the LGI for the pure qubit is more robust than that of the qubit with driven. Moreover, in the case of a qubit that is subjected to driving and is in the presence of dissipation and dephasing, the robustness of quantum violations of the LGI for these scenario systems will become vulnerable, with the driven intensity and the rate of spontaneous emission increasing, respectively, for coarsening measurement both in reference and in final resolution. In addition, in the energy constraint and the projective measurement, the LGI can attain its maximum violation value, 1.5, for the coherent dynamics; while for drive, dissipative and dephasing qubits, the LGI cannot attain the value of 1.5. For systems in the presence of dissipation and dephasing, we find that in the energy constraint, the robustness of the coarsening measurement in final resolution exhibits more vulnerable than that of the coarsening measurement in reference. And for systems with drive and without drive, the robustness of the coarsening measurement in temporal reference is the most robust, and the robustness of the coarsening of measurement final measurement resolution is the most vulnerable.
在本文中，我们考虑一个量子比特在四种情形下的情况：有驱动、无驱动、存在耗散和退相，以研究在能量约束下莱格特 - 加 Garg 不等式（LGI）的量子违背情况。在能量约束的情况下，我们发现在参考和最终分辨率的粗化测量下，纯量子比特的 LGI 的量子违背最为稳健；另一方面，退相量子比特的 LGI 的量子违背最为脆弱，而有驱动量子比特的 LGI 的量子违背则介于纯量子比特和耗散量子比特之间。在测量时间参考的粗化下，纯量子比特的 LGI 的量子违背比有驱动的量子比特更稳健。此外，对于一个受到驱动且存在耗散和退相的量子比特，在参考和最终分辨率的粗化测量中，随着驱动强度和自发发射率分别增加，这些情形系统的 LGI 的量子违背的稳健性将变得脆弱。另外，在能量约束和投影测量中，对于相干动力学，LGI 可以达到其最大违背值 1.5；而对于有驱动、耗散和退相的量子比特，LGI 无法达到 1.5 的值。对于存在耗散和退相的系统，我们发现在能量约束下，最终分辨率的粗化测量的稳健性比参考中的粗化测量表现得更脆弱。并且对于有驱动和无驱动的系统，时间参考中的粗化测量的稳健性最强，而最终测量分辨率的粗化的稳健性最脆弱。
