Manipulating the measured uncertainty under Lee−Yang dephasing channels through local \mathcal{P}\mathcal{T}-symmetric operations

Abstract

Uncertainty relation lies at the heart of quantum physics, which is one of the fundamental characteristics of quantum mechanics. With the advent of quantum information theory, entropic uncertainty relation was proposed, which plays an important and irreplaceable role in quantum information science. In this work, we attempt to observe dynamics of entropic uncertainty in the presence of quantum memory under two different types of Lee−Yang dephasing channels. It is interesting to find that the dephasing channels have a negative effect on decreasing the uncertainty and the analogous partition function is anti-correlated with the uncertainty. In addition, we here propose an effective strategy to manipulate the uncertainty of interest of the subsystem by performing a parity-time symmetric (\mathcal{P}\mathcal{T}-symmetric) operation. It is worth noting that the uncertainty of measurement will be reduced to a certain extent by properly modulating the \mathcal{P}\mathcal{T}-symmetric operations under the considered channels. In this sense, we argue that our explorations offer insight into dynamics of entropic uncertainty in typical Lee−Yang dephasing channels, and might be beneficial to quantum measurement estimation in practical quantum systems.

Graphical abstract

Keywords

entropic uncertainty relation / quantum correlation / ${\color{[RGB]{12,108,100}}{{\cal {PT}}}} $-symmetric operation

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Acknowledgements

This study was supported by the National Natural Science Foundation of China (Grant Nos. 12075001 and 12175001), Anhui Provincial Key Research and Development Plan (Grant No. 2022b13020004), Anhui Provincial Natural Science Foundation (Grant No. 1508085QF139), and the Fund of the CAS Key Laboratory of Quantum Information (Grant No. KQI201701).

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