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Probing entropic uncertainty relations under a two-atom system coupled with structured bosonic reservoirs

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Abstract

The uncertainty principle imposes constraints on an observer’s ability to make precision measurements for two incompatible observables; thus, uncertainty relations play a key role in quantum precision measurement in the field of quantum information science. Here, our aim is to examine non-Markovian effects on quantum-memory-assisted entropic uncertainty relations in a system consisting of two atoms coupled with structured bosonic reservoirs. Explicitly, we explore the dynamics of the uncertainty relations via entropic measures in non-Markovian regimes when two atomic qubits independently interact with their own infinite degree-of-freedom bosonic reservoir. We show that measurement uncertainty vibrates with periodically increasing amplitude with growing non-Markovianity of the observed system and ultimately saturates toward a fixed value at a long time limit. It is worth noting that there are several appealing conclusions raised by us: First, the uncertainty’s lower bound does not entirely depend on the quantum correlations within the two-qubit system, being affected by an interplay between the quantum discord and the minimal von Neumann conditional entropy \(\mathcal{S}_\mathrm{ce}\). Second, the dynamic characteristic of the measurement uncertainty is considerably distinctive with regard to Markovian and non-Markovian regimes, respectively. Third, the measurement uncertainty is closely correlated with the Bell non-locality \({\mathcal{B}}\). Moreover, we claim that the entropic uncertainty relation could be a promising tool with which to probe entanglement in current architecture.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 61601002 and 11575001), Anhui Provincial Natural Science Foundation (Grant No. 1508085QF139), and the Fund of CAS Key Laboratory of Quantum Information (Grant No. KQI201701).

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Authors and Affiliations

  1. School of Physics and Material Science, Anhui University, Hefei, 230601, China

    Dong Wang, Wei-Nan Shi, Fei Ming, Wen-Yang Sun & Liu Ye

  2. CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China

    Dong Wang

  3. Department of Chemistry, Department of Physics and Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907, USA

    Ross D. Hoehn & Sabre Kais

  4. Santa Fe Institute, Santa Fe, NM, 87501, USA

    Sabre Kais

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  1. Dong Wang
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Wang, D., Shi, WN., Hoehn, R.D. et al. Probing entropic uncertainty relations under a two-atom system coupled with structured bosonic reservoirs. Quantum Inf Process 17, 335 (2018). https://doi.org/10.1007/s11128-018-2100-x

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