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Hierarchy, factorization law of two measurement-induced nonlocalities and their performances in quantum phase transition

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Abstract

There are two measurement-induced nonlocalities, which are, respectively, defined via the trace norm (MIN-1) and Hilbert–Schmidt norm (MIN-2). We investigate the hierarchy relation and factorization law of them. Their performances in quantum phase transition have also been explored. For X-shape states, a rigorous hierarchy relation is established between two MINs. When two qubits, which are initially prepared in an X-shape state, interact independently with the corresponding multimode vacuum reservoirs, the evolutions of two MINs satisfy the factorization law. With quantum renormalization group method, it is found that two MINs can signify the criticality of the spin system while the position where the derivative of MIN-1 takes the minimum value is always larger than that where the derivative of MIN-2 takes the minimum value. Therefore, MIN-1 is more suitable to identify the critical point of quantum phase transition.

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Acknowledgments

This work was supported by the Foundation Research Project (Natural Science Foundation) of Jiangsu Province under Grant No. BK20140214 and the National Natural Science Foundation of China under Grant Nos. 61401465 and 11375168.

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  1. Department of Physics, China University of Mining and Technology, Xuzhou, 221116, China

    Liang Qiu & Zhi Liu

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  1. Liang Qiu
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  2. Zhi Liu
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Correspondence to Liang Qiu.

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Qiu, L., Liu, Z. Hierarchy, factorization law of two measurement-induced nonlocalities and their performances in quantum phase transition. Quantum Inf Process 15, 2053–2065 (2016). https://doi.org/10.1007/s11128-016-1256-5

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