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Correlation Property of Multipartite Quantum Image

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Abstract

Inspired on the classical Bayesian method also called mutual information, by generalizing the classical case to quantum approach to study the multipartite correlation in quantum image by using the flexible representation of quantum images (FRQI) method. Some important entanglement measures are calculated including von Neumann entropy, conditional entropy, joint entropy, discord and mutual information. We take two typical images of size 2 × 2 pixels and 8 × 8 pixels and study their entanglement measures from different classical and quantum point of view. The quantum image of size 2 × 2 is studied under the change of color for one pixel, but the quantum image of 8 × 8 is treated under translation transform. We find that the classical joint entropy remains invariant under the change of color for one pixel but the quantum entropy is sensitive to such change. It is shown that the total correlation IT could arrive to the double amount of the classical joint entropy. The discord in the classical case is zero, but it varies much in the quantum case.

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Notes

  1. These two measures are also used in classical image fusion that is an important application in medical physics [22, 23, 26].

  2. We often use S and H denote the quantum and classical entropy, respectively.

  3. It should be emphasized that the entropy S is calculated by considering the binary logarithm (the base is taken 2 but not natural number e), and the units of entropy S are expressed in bits.

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Acknowledgments

This work is supported by project 20190234-SIP-IPN, COFAA-IPN, Mexico and partially by the CONACYT project under grant No. 288856-CB-2016.

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Authors and Affiliations

  1. Laboratorio de Información Cuántica, CIDETEC, Instituto Politécnico Nacional, UPALM, CDMX, 07700, Mexico

    M. A. Mercado Sanchez & Shi-Hai Dong

  2. Catedrática CONACYT, CIC, Instituto Politécnico Nacional, CDMX, 07700, Mexico

    Guo-Hua Sun

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  1. M. A. Mercado Sanchez
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  2. Guo-Hua Sun
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  3. Shi-Hai Dong
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Correspondence to Shi-Hai Dong.

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Sanchez, M.A.M., Sun, GH. & Dong, SH. Correlation Property of Multipartite Quantum Image. Int J Theor Phys 58, 3773–3796 (2019). https://doi.org/10.1007/s10773-019-04247-9

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