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Quantum-memory-assisted entropic uncertainty in two-qubit Heisenberg XYZ chain with Dzyaloshinskii–Moriya interactions and effects of intrinsic decoherence

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Abstract

Quantum-memory-assisted entropic uncertainty relation (QMA-EUR) in two-qubit Heisenberg XYZ spin chain model with Dzyaloshinskii–Moriya (DM) interaction has been investigated. The paper shows that the DM interactions and the spin interactions alone x, y, z directions can efficiently suppress the entropic uncertainty of Pauli observables (\(\sigma _{x}\) and \(\sigma _{z}\)), even make the entropic uncertainty close to zero. As well, it is pointed out that the entropic uncertainty reaches to zero at very low temperature, starts to increase with temperature after a threshold, and generally becomes constant at a fixed value. We also verified the Bob’s uncertainty about Alice’s measurement outcomes is anticorrelated with the sum of the accessible information of observer. Furthermore, the decoherence conditions including dephasing and noisy environments are considered. For the fixed initial state, the entropic uncertainty of the XYZ model with DM interaction in z-direction are independent of spin–spin coupling \(J_z\) and the anisotropy parameter \(\varDelta \). In the dephasing environment, the evolutions of entropic uncertainty and its lower bound \(U_{B}\) oscillate with the time and saturates at a finite value, and this value is varied with the purity parameter r of initial state. In the noisy environment, the entropic uncertainty and its lower bound monotonically increase with the time and will be stable at value 2 quickly. This is because the combined effects of the DM interaction and the decoherence force the various initial entanglement states to oscillate into an identical state, regardless of the value of \(D_{z}\) and the parameter r of initial state.

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Acknowledgements

The work was supported by the National Natural Science Foundation of China under Grant No.11464015 and No.11374096 , the Natural Science Foundation of Hunan Province under Grant No.14jj6035, the Science Research Foundation of Education Department of Hunan Province under Grant No.14B147.

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Authors and Affiliations

  1. School of Software, Jishou University, Zhangjiajie, 427000, China

    Yanliang Zhang, Qingping Zhou & Guodong Kang

  2. Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, College of Physics and Information Science, Hunan Normal University, Changsha, 410081, China

    Maofa Fang & Xiaowu Li

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  1. Yanliang Zhang
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  2. Qingping Zhou
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Correspondence to Yanliang Zhang.

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Zhang, Y., Zhou, Q., Fang, M. et al. Quantum-memory-assisted entropic uncertainty in two-qubit Heisenberg XYZ chain with Dzyaloshinskii–Moriya interactions and effects of intrinsic decoherence. Quantum Inf Process 17, 326 (2018). https://doi.org/10.1007/s11128-018-2088-2

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