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Exploring entropic uncertainty relation in the Heisenberg XX model with inhomogeneous magnetic field

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Abstract

In this work, we investigate the quantum-memory-assisted entropic uncertainty relation in a two-qubit Heisenberg XX model with inhomogeneous magnetic field. It has been found that larger coupling strength J between the two spin-chain qubits can effectively reduce the entropic uncertainty. Besides, we observe the mechanics of how the inhomogeneous field influences the uncertainty, and find out that when the inhomogeneous field parameter \(b<1\), the uncertainty will decrease with the decrease of the inhomogeneous field parameter b, conversely, the uncertainty will increase with decreasing b under the condition that \(b>1\). Intriguingly, the entropic uncertainty can shrink to zero when the coupling coefficients are relatively large, while the entropic uncertainty only reduces to 1 with the increase of the homogeneous magnetic field. Additionally, we observe the purity of the state and Bell non-locality and obtain that the entropic uncertainty is anticorrelated with both the purity and Bell non-locality of the evolution state.

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Acknowledgements

This work was supported by the National Science Foundation of China under Grant Nos. 11575001 and 61601002 and Anhui Provincial Natural Science Foundation under Grant No. 1508085QF139.

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Authors and Affiliations

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

    Ai-Jun Huang, Dong Wang, Jia-Ming Wang, Jia-Dong Shi, Wen-Yang Sun & Liu Ye

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

    Dong Wang

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  1. Ai-Jun Huang
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  2. Dong Wang
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Correspondence to Dong Wang.

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Huang, AJ., Wang, D., Wang, JM. et al. Exploring entropic uncertainty relation in the Heisenberg XX model with inhomogeneous magnetic field. Quantum Inf Process 16, 204 (2017). https://doi.org/10.1007/s11128-017-1657-0

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