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Volume 10 Issue 2
Feb.  2023

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2023  >  10(2): 439-450
Y. Y. Zhao, F. Y. Xiao, M. Aritsugi, and W. P. Ding, “A quantum Tanimoto coefficient fidelity for entanglement measurement,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 2, pp. 439–450, Feb. 2023. doi: 10.1109/JAS.2022.106079
Citation: Y. Y. Zhao, F. Y. Xiao, M. Aritsugi, and W. P. Ding, “A quantum Tanimoto coefficient fidelity for entanglement measurement,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 2, pp. 439–450, Feb. 2023. doi: 10.1109/JAS.2022.106079
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A Quantum Tanimoto Coefficient Fidelity for Entanglement Measurement

doi: 10.1109/JAS.2022.106079
  • 1.

    School of Big Data and Software Engineering, Chongqing University, Chongqing 401331, China

  • 2.

    Faculty of Advanced Science and Technology, Kumamoto University, Kumamoto 860-8555, Japan

  • 3.

    School of Information and Technology, Nantong University, Nantong 223019, China

Funds:  This work was supported by the National Natural Science Foundation of China (62003280, 61976120), Chongqing Talents: Exceptional Young Talents Project (cstc2022ycjh-bgzxm0070), Natural Science Foundation of Chongqing (2022NSCQ-MSX2993), Natural Science Key Foundation of Jiangsu Education Department (21KJA510004), and Chongqing Overseas Scholars Innovation Program (cx2022024)
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    Abstract
  • Fidelity plays an important role in quantum information processing, which provides a basic scale for comparing two quantum states. At present, one of the most commonly used fidelities is Uhlmann-Jozsa (U-J) fidelity. However, U-J fidelity needs to calculate the square root of the matrix, which is not trivial in the case of large or infinite density matrices. Moreover, U-J fidelity is a measure of overlap, which has limitations in some cases and cannot reflect the similarity between quantum states well. Therefore, a novel quantum fidelity measure called quantum Tanimoto coefficient (QTC) fidelity is proposed in this paper. Unlike other existing fidelities, QTC fidelity not only considers the overlap between quantum states, but also takes into account the separation between quantum states for the first time, which leads to a better performance of measure. Specifically, we discuss the properties of the proposed QTC fidelity. QTC fidelity is compared with some existing fidelities through specific examples, which reflects the effectiveness and advantages of QTC fidelity. In addition, based on the QTC fidelity, three discrimination coefficients ${\boldsymbol{d_1^{{\bf{QTC}}} }}$, ${\boldsymbol{d_2^{{\bf{QTC}}}}}$, and ${\boldsymbol{d_3^{{\bf{QTC}}}}}$ are defined to measure the difference between quantum states. It is proved that the discrimination coefficient ${\boldsymbol{d_3^{{\bf{QTC}}} }}$ is a true metric. Finally, we apply the proposed QTC fidelity-based discrimination coefficients to measure the entanglement of quantum states to show their practicability.

     

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    • Yangyang Zhao and Weiping Ding contributed equally to this work.
    References(50)
  • [1]
    C. Chamberland, K. Noh, Arrangoiz-Arriola, E. T. Campbell, C. T. Hann, J. Iverson, H. Putterman, T. C. Bohdanowicz, S. T. Flammia, A. Keller, G. Refael, J. Preskill, L. Jiang, A. H. Safavi-Naeini, O. Painter, and F. G. S. L. Brandão, “Building a fault-tolerant quantum computer using concatenated cat codes,” PRX Quantum, vol. 3, no. 1, p. 010329, Feb. 2022. doi: 10.1103/PRXQuantum.3.010329
    [2]
    N. Ghaeminezhad and S. Cong, “Preparation of hadamard gate for open quantum systems by the Lyapunov control method,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 3, pp. 733–740, May 2018. doi: 10.1109/JAS.2018.7511084
    [3]
    W. R. Zhang, “Ground-0 axioms vs. first principles and second law: From the geometry of light and logic of photon to mind-light-matter unity-AI&QI,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 3, pp. 534–553, Mar. 2021. doi: 10.1109/JAS.2021.1003868
    [4]
    D. Wu, Q. Zhao, X. M. Gu, H. S. Zhong, Y. Zhou, L. C. Peng, J. Qin, Y. H. Luo, K. Chen, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Robust self-testing of multiparticle entanglement,” Phys. Rev. Lett., vol. 127, no. 23, p. 230503, Dec. 2021. doi: 10.1103/PhysRevLett.127.230503
    [5]
    J. W. Lai and K. H. Cheong, “Chaotic switching for quantum coin Parrondo’s games with application to encryption,” Phys. Rev. Res., vol. 3, no. 2, p. L022019, Jun. 2021. doi: 10.1103/PhysRevResearch.3.L022019
    [6]
    F. Y. Xiao and W. Pedrycz, “Negation of the quantum mass function for multisource quantum information fusion with its application to pattern classification,” IEEE Trans. Pattern Anal. Mach. Intell., 2022. DOI: 10.1109/TPAMI.2022.3167045.
    [7]
    F. Y. Xiao, Z. H. Cao, and C. T. Lin, “A complex weighted discounting multisource information fusion with its application in pattern classification,” IEEE Trans. Knowl. Data Eng., 2022. DOI: 10.1109/TKDE.2022.3206871.
    [8]
    C. D. Xiang, S. Ma, S. Kuang, and D. Y. Dong, “Coherent H∞ control for linear quantum systems with uncertainties in the interaction Hamiltonian,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 2, pp. 432–440, Feb. 2020.
    [9]
    Z. Wang, S. X. Liu, R. G. Wang, L. L. Yuan, J. Huang, Y. Y. Zhai, and S. Zou, “Atomic spin polarization controllability analysis: A novel controllability determination method for spin-exchange relaxation-free co-magnetometers,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 4, pp. 699–708, Apr. 2022. doi: 10.1109/JAS.2021.1004383
    [10]
    F. Y. Xiao, “Generalized quantum evidence theory,” Appl. Intell., 2022. DOI: 10.1007/s10489-022-04181-0.
    [11]
    L. T. Zheng and F. Y. Xiao, “Complex interval number-based uncertainty modeling method with its application in decision fusion,” Int. J. Intell. Syst., 2022. DOI: 10.1002/int.23070.
    [12]
    K. H. Cheong, D. B. Saakian, and R. Zadourian, “Allison mixture and the two-envelope problem,” Phys. Rev. E, vol. 96, no. 6, p. 062303, Dec. 2017.
    [13]
    W. Ding, C. T. Lin, and Z. H. Cao, “Deep neuro-cognitive co-evolution for fuzzy attribute reduction by quantum leaping PSO with nearest-neighbor memeplexes,” IEEE Trans. Cybern., vol. 49, no. 7, pp. 2744–2757, Jul. 2019. doi: 10.1109/TCYB.2018.2834390
    [14]
    J. W. Lai and K. H. Cheong, “Parrondo effect in quantum coin-toss simulations,” Phys. Rev. E, vol. 101, no. 5, p. 052212, May 2020. doi: 10.1103/PhysRevE.101.052212
    [15]
    Y. Deng, “Random permutation set,” Int. J. Comput. Commun. Control, vol. 17, no. 1, p. 4542, Jan. 2022.
    [16]
    Y. T. Song and Y. Deng, “Entropic explanation of power set,” Int. J. Comput. Commun. Control, vol. 16, no. 4, p. 4413, Aug. 2021.
    [17]
    J. X. Deng and Y. Deng, “Maximum entropy of random permutation set,” Soft Comput., vol. 26, no. 21, pp. 11265–11275, Nov. 2022. doi: 10.1007/s00500-022-07351-x
    [18]
    A. U. Rahman, S. Haddadi, M. R. Pourkarimi, and M. Ghominejad, “Fidelity of quantum states in a correlated dephasing channel,” Laser Phys. Lett., vol. 19, no. 3, p. 035204, Feb. 2022. doi: 10.1088/1612-202X/ac5040
    [19]
    H. Wang, H. Hu, T. H. Chung, J. Qin, X. X. Yang, J. Li, R. Z. Liu, H. S. Zhong, Y. M. He, X. Ding, Y. H. Deng, Q. Dai, Y. H. Huo, S. Höfling, C. Y. Lu, and J. W. Pan, “On-demand semiconductor source of entangled photons which simultaneously has high fidelity, efficiency, and indistinguishability,” Phys. Rev. Lett., vol. 122, no. 11, p. 113602, Mar. 2019. doi: 10.1103/PhysRevLett.122.113602
    [20]
    M. McEwen, D. Kafri, Z. Chen, J. Atalaya, K. J. Satzinger, C. Quintana, V. Klimov, D. Sank, C. Gidney, A. G. Fowler, F. Arute, K. Arya, B. Buckley, B. Burkett, N. Bushnell, B. Chiaro, R. Collins, S. Demura, A. Dunsworth, C. Erickson, B. Foxen, M. Giustina, T. Huang, S. Hong, E. Jeffrey, S. Kim, K. Kechedzhi, F. Kostritsa, Laptev, A. Megrant, X. Mi, J. Mutus, O. Naaman, M. Neeley, C. Neill, M. Niu, A. Paler, N. Redd, Roushan, T. C. White, J. Yao, Y eh, A. Zalcman, Y. Chen, V. N. Smelyanskiy, J. M. Martinis, H. Neven, J. Kelly, A. N. Korotkov, A. G. Petukhov, and R. Barends, “Removing leakage-induced correlated errors in superconducting quantum error correction,” Nat. Commun., vol. 12, no. 1, p. 1761, Mar. 2021. doi: 10.1038/s41467-021-21982-y
    [21]
    Y. L. Chi, J. S. Huang, Z. C. Zhang, J. Mao, Z. N. Zhou, X. J. Chen, C. H. Zhai, J. M. Bao, T. X. Dai, H. H. Yuan, M. Zhang, D. X. Dai, B. Tang, Y. Yang, Z. H. Li, Y. H. Ding, L. K. Oxenløwe, M. G. Thompson, J. L. O’brien, Y. Li, Q. H. Gong, and J. W. Wang, “A programmable qudit-based quantum processor,” Nat. Commun., vol. 13, no. 1, p. 1166, Mar. 2022. doi: 10.1038/s41467-022-28767-x
    [22]
    V. Vedral and M. B. Plenio, “Entanglement measures and purification procedures,” Phys. Rev. A, vol. 57, no. 3, pp. 1619–1633, Mar. 1998. doi: 10.1103/PhysRevA.57.1619
    [23]
    L. M. Gao, F. L. Yan, and T. Gao, “Monogamy of entanglement measures based on fidelity in multiqubit systems,” Quantum Inf. Process., vol. 20, no. 10, p. 332, Oct. 2021. doi: 10.1007/s11128-021-03268-w
    [24]
    R. Jozsa, “Fidelity for mixed quantum states,” J. Mod. Opt., vol. 41, no. 12, pp. 2315–2323, Dec. 1994. doi: 10.1080/09500349414552171
    [25]
    A. Uhlmann, “The ‘transition probability’ in the state space of a *-algebra,” Rep. Math. Phys., vol. 9, no. 2, pp. 273–279, Apr. 1976. doi: 10.1016/0034-4877(76)90060-4
    [26]
    Y. C. Liang, Y. H. Yeh, E. Mendonça, R. Y. Teh, M. D. Reid, and D. Drummond, “Quantum fidelity measures for mixed states,” Rep. Prog. Phys., vol. 82, no. 7, p. 076001, Jun. 2019. doi: 10.1088/1361-6633/ab1ca4
    [27]
    J. L. Chen, L. B. Fu, A. A. Ungar, and X. G. Zhao, “Alternative fidelity measure between two states of an N-state quantum system,” Phys. Rev. A, vol. 65, no. 5, p. 054304, May 2002. doi: 10.1103/PhysRevA.65.054304
    [28]
    E. Mendonça, R. D. J. Napolitano, M. A. Marchiolli, C. J. Foster, and Y. C. Liang, “Alternative fidelity measure between quantum states,” Phys. Rev. A, vol. 78, no. 5, p. 052330, Nov. 2008. doi: 10.1103/PhysRevA.78.052330
    [29]
    Z. H. Ma, F. L. Zhang, and J. L. Chen, “Geometric interpretation for the A fidelity and its relation with the bures fidelity,” Phys. Rev. A, vol. 78, no. 6, p. 064305, Dec. 2008. doi: 10.1103/PhysRevA.78.064305
    [30]
    X. G. Wang, C. S. Yu, and X. X. Yi, “An alternative quantum fidelity for mixed states of qudits,” Phys. Lett. A, vol. 373, no. 1, pp. 58–60, Dec. 2008. doi: 10.1016/j.physleta.2008.10.083
    [31]
    A. Ektesabi, N. Behzadi, and E. Faizi, “Improved bound for quantum-speed-limit time in open quantum systems by introducing an alternative fidelity,” Phys. Rev. A, vol. 95, no. 2, p. 022115, Feb. 2017. doi: 10.1103/PhysRevA.95.022115
    [32]
    B. Schumacher, “Quantum coding,” Phys. Rev. A, vol. 51, no. 4, pp. 2738–2747, Apr. 1995. doi: 10.1103/PhysRevA.51.2738
    [33]
    Y. Deng, “Uncertainty measure in evidence theory,” Sci. China Inf. Sci., vol. 63, no. 11, p. 210201, Oct. 2020. doi: 10.1007/s11432-020-3006-9
    [34]
    Y. Deng, “Information volume of mass function,” Int. J. Comput. Commun. Control, vol. 15, no. 6, p. 3983, Oct. 2020.
    [35]
    D. J. Rogers and T. T. Tanimoto, “A computer program for classifying plants: The computer is programmed to simulate the taxonomic process of comparing each case with every other case,” Science, vol. 132, no. 3434, pp. 1115–1118, Oct. 1960. doi: 10.1126/science.132.3434.1115
    [36]
    F. Y. Xiao, J. H. Wen, and W. Pedrycz, “Generalized divergence-based decision making method with an application to pattern classification,” IEEE Trans. Knowl. Data Eng., 2022. DOI: 10.1109/TKDE.2022.3177896.
    [37]
    W. T. Fan and F. Y. Xiao, “A complex Jensen-Shannon divergence in complex evidence theory with its application in multi-source information fusion,” Eng. Appl. Artif. Intell., vol. 116, p. 105362, Nov. 2022. doi: 10.1016/j.engappai.2022.105362
    [38]
    F. Y. Xiao, “GEJS: A generalized evidential divergence measure for multisource information fusion,” IEEE Trans. Syst. Man Cybern. Syst., 2022. DOI: 10.1109/TSMC.2022.3211498.
    [39]
    C. S. Zhu, F. Y. Xiao, and Z. H. Cao, “A generalized Rényi divergence for multi-source information fusion with its application in EEG data analysis,” Inf. Sci., vol. 605, pp. 225–243, Aug. 2022. doi: 10.1016/j.ins.2022.05.012
    [40]
    Z. Deng and J. Y. Wang, “A new evidential similarity measurement based on tanimoto measure and its application in multi-sensor data fusion,” Eng. Appl. Artif. Intell., vol. 104, p. 104380, Sept. 2021. doi: 10.1016/j.engappai.2021.104380
    [41]
    F. Huber, S. van der Burg, J. J. J. van der Hooft, and L. Ridder, “Ms2deepscore: A novel deep learning similarity measure to compare tandem mass spectra,” J. Cheminf., vol. 13, no. 1, p. 84, Oct. 2021. doi: 10.1186/s13321-021-00558-4
    [42]
    S. Ray and P. M. Alsing, “The Hilbert Schmidt inner product: Quantum illumination and beyond,” in Proc. SPIE 11167, Quantum Technologies and Quantum Information Science V, Strasbourg, France, 2019, pp. 111670G.
    [43]
    I. J. Schoenberg, “Metric spaces and positive definite functions,” Trans. Am. Math. Soc., vol. 44, no. 3, pp. 522–536, Jan. 1938. doi: 10.1090/S0002-9947-1938-1501980-0
    [44]
    D. Bures, “An extension of Kakutani’s theorem on infinite product measures to the tensor product of semifinite w*-algebras,” Trans. Am. Math. Soc., vol. 135, pp. 199–212, Jan. 1969.
    [45]
    Y. Inui and Y. Yamamoto, “Entanglement and photon anti-bunching in coupled non-degenerate parametric oscillators,” Entropy, vol. 23, no. 5, p. 624, May 2021. doi: 10.3390/e23050624
    [46]
    Z. T. Qi, Y. H. Li, Y. W. Huang, J. Feng, Y. L. Zheng, and X. F. Chen, “A 15-user quantum secure direct communication network,” Light Sci. Appl., vol. 10, no. 1, p. 183, Sept. 2021. doi: 10.1038/s41377-021-00634-2
    [47]
    S. Aaronson, J. H. Liu, Q. P. Liu, M. Zhandry, and R. Z. Zhang, “New approaches for quantum copy-protection,” in Proc. 41st Annu. Int. Cryptology Conf. Advances in Cryptology, 2021, pp. 526–555.
    [48]
    Y. Alexeev, D. Bacon, K. R. Brown, R. Calderbank, L. D. Carr, F. T. Chong, B. DeMarco, D. Englund, E. Farhi, B. Fefferman, A. V. Gorshkov, A. Houck, J. Kim, S. Kimmel, M. Lange, S. Lloyd, M. D. Lukin, D. Maslov, Maunz, C. Monroe, J. Preskill, M. Roetteler, M. J. Savage, and J. Thompson, “Quantum computer systems for scientific discovery,” PRX Quantum, vol. 2, no. 1, p. 017001, Feb. 2021. doi: 10.1103/PRXQuantum.2.017001
    [49]
    T. X. Dai, Y. T. Ao, J. M. Bao, J. Mao, Y. L. Chi, Z. R. Fu, Y. L. You, X. J. Chen, C. H. Zhai, B. Tang, Y. Yang, Z. H. Li, L. Q. Yuan, F. Gao, X. Lin, M. G. Thompson, J. L. O’brien, Y. Li, X. Y. Hu, Q. H. Gong, and J. W. Wang, “Topologically protected quantum entanglement emitters,” Nat. Photonics, vol. 16, no. 3, pp. 248–257, Feb. 2022. doi: 10.1038/s41566-021-00944-2
    [50]
    R. Horodecki, “Two-spin-12 mixtures and Bell’s inequalities,” Phys. Lett. A, vol. 210, no. 4–5, pp. 223–226, Jan. 1996. doi: 10.1016/0375-9601(95)00904-3
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    Highlights

    • A novel QTC fidelity that considers both overlap and separation between quantum states is proposed
    • Three discrimination coefficients are proposed for quantum states based on QTC fidelity
    • The QTC fidelity-based discrimination coefficients are applied to measure entanglement

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