隨著量子力學不斷的發展以來，人們一直試圖在與經典力學之間劃下清楚的界限，並且尋找在量子資訊中的應用，引起了無數研究者的興趣。其中量子操縱性是量子資訊理論中重要的非經典資源，它已經引起了無數研究者的研究興趣。其中，對於一任意的雙量子位元狀態，人們已提出了許多操縱性標準和量化可操縱性的程度。然而，儘管對集合的可否引導性已經有足夠的標準來確立，但如何檢測任意量子態的可引導性程度仍然不清楚。因為當考慮對可能的測量設置進行優化時，就需要經過無限多次的SDP測試，由於這涉及到對所有可能的不相容的測量設置進行繁瑣的優化。
在這項研究中，我們期望利用機器學習能在大量數據中分析隱藏模式的能力來簡化複雜的物理問題。在這裡，我們建構了機器學習的模型，即人工神經元網絡（ANN），為任何量子位元狀態提供一個高效的量子可操縱性檢測方案。
在過去的研究中，我們制定了SDP的計算協議，以產生具有相對應標籤的訓練數據集。此外，我們對密度矩陣做了特徵工程，轉換成五種不同的特徵來比較性能，並分析了兩種特定量子態和隨機量子態，同時預測了在優化測量設置的情況下的可操縱性程度。我們的最終表明，根據訓練完善的有效模型對不同編碼方式的物理特徵反應，我們識別出，在探討愛麗絲是否能操控勃的情況最有效的特徵，即為經過消除偏度過後的愛麗絲規則排列的轉向橢圓體。

Since the development of quantum mechanics, there has been an attempt to
draw the line between classical mechanics and the search for applications in quantum information has attracted the interest of countless researchers. One of the quantum steering is an outstanding non-classical resource in quantum information theory, it has attracted increasing research attention. Not only numerous steering criteria and quantify the steerability have been proposed for an arbitrary two-qubit state. Although the characterization of the steerability of the ensemble is well established, it remains unclear how to detect the degree of steerability of an arbitrary quantum bit-pair state. Since, when consider the optimization over possible measurement settings, it remains quite difficult which involves tedious optimization of all possible incompatible measurements.
In this work, we expect through the machine learning ability of identifying hidden patterns in a large amount of data to solve complex physics problems. Here,
we apply a machine learning approach called Artificial Neuron Network (ANN) to
provide an efficient quantum detection protocol for any quantum states. In previous work we have customized the SDP calculation protocol to generate labelled
training data sets. In addition, we do feature engineering on the density matrix
into five different features to compare the performance and analyzed two different
types of specific quantum states and random quantum states, meanwhile predicting the degree of steerability when in situations of optimization measurement settings.
According to the responses of the well-trained models to the different physics
driven features encoding the states to be recognized, we can identify the most
efficient characterization whether Alice steering Bob situation is dependent on
in terms of Alice’s regularly aligned steering ellipsoid and eliminate the skews in
steering ellipsoid will not affect the steerability.

[1] A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete ?” Phys. Rev. 47, 777 (1935).
[2] E. Schrödinger, “Discussion of probability relations between separated systems,”Mathematical Proceedings of the Cambridge Philosophical Society 31, 555–563 (1935).
[3] R. Uola, A. C. S. Costa, H. C. Nguyen, and O. Gühne, “Quantum steering,” Rev. Mod. Phys. 92, 015001 (2020).
[4] J. S. Bell, “On the einstein podolsky rosen paradox,” Physics Physique Fizika 1, 195 (1964).
[5] A. Aspect, P. Grangier, and G. Roger, “Experimental realization of einstein podolsky-rosen-bohm gedankenexperiment: A new violation of bell’s inequalities,”Phys. Rev. Lett. 49, 91 (1982).
[6] A. Aspect, J. Dalibard, and G. Roger, “Experimental test of bell’s inequalities using time-varying analyzers,” Phys. Rev. Lett. 49, 1804 (1982).
[7] S. J. Freedman and J. F. Clauser, “Experimental test of local hidden-variable theories,” Phys. Rev. Lett. 28, 938 (1972).
[8] M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-k. Larsson, C. Abellan, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-loopholefree test of bell's theorem with entangled photons,” Phys. Rev. Lett. 115, 250401 (2015).
[9] B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. Vermeulen, R. N. Schouten, C. Abellán, et al., “Loophole-free bell inequalityviolation using electron spins separated by 1.3 kilometres,” Nature 526, 682 (2015).
[10] H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, entanglement, nonlocality, and the einstein-podolsky-rosen paradox,” Phys. Rev. Lett. 98, 140402 (2007).
[11] D. Cavalcanti and P. Skrzypczyk, “Quantum steering: a review with focus on semidefinite programming,” Reports on Progress in Physics 80, 024001 (2016).
[12] R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865 (2009).
[13] M. Horodecki, P. Horodecki, and R. Horodecki, “Separability of n-particle mixed states: necessary and sufficient conditions in terms of linear maps,” Physics Letters A 283, 1 (2001).
[14] A. Peres, “Separability criterion for density matrices,” Phys. Rev. Lett. 77, 1413 (1996).
[15] B. Mahesh, “Machine learning algorithms-a review,” International Journal of Science and Research (IJSR).[Internet] 9, 381 (2020).
[16] B. Bochenek and Z. Ustrnul, “Machine learning in weather prediction and climate analysesmdash;applications and perspectives,” Atmosphere 13 (2022), 10.3390/atmos13020180.
[17] W. Huang, T. W. Ying, W. L. C. Chin, L. Baskaran, O. E. H. Marcus, K. K. Yeo, and N. S. Kiong, “Application of ensemble machine learning algorithms on lifestyle factors and wearables for cardiovascular risk prediction,” Scientific Reports 12, 1033 (2022).
[18] M. Chieregato, F. Frangiamore, M. Morassi, C. Baresi, S. Nici, C. Bassetti, C. Bnà, and M. Galelli, “A hybrid machine learning/deep learning covid-19 severity predictive model from ct images and clinical data,” Scientific reports 12, 1 (2022).
[19] S. J. Mambou, P. Maresova, O. Krejcar, A. Selamat, and K. Kuca, “Breast cancer detection using infrared thermal imaging and a deep learning model,” Sensors 18 (2018), 10.3390/s18092799.
[20] M. Diwakar, A. Tripathi, K. Joshi, M. Memoria, P. Singh, and N. kumar, “Latest trends on heart disease prediction using machine learning and image fusion,”Materials Today: Proceedings 37, 3213 (2021), international Conference on Newer Trends and Innovation in Mechanical Engineering: Materials Science.
[21] H. Zhang, L. Li, K. Qiao, L. Wang, B. Yan, L. Li, and G. Hu, “Image prediction for limited-angle tomography via deep learning with convolutional neural network,”arXiv preprint arXiv:1607.08707 (2016), 10.48550/arXiv.1607.08707.
[22] A. Singh, N. Thakur, and A. Sharma, “A review of supervised machine learningalgorithms,” , 1310 (2016).
[23] M. Chen, U. Challita, W. Saad, C. Yin, and M. Debbah, “Artificial neural networksbased machine learning for wireless networks: A tutorial,” IEEE Communications Surveys Tutorials 21, 3039 (2019).
[24] E. G. Cavalcanti, S. J. Jones, H. M. Wiseman, and M. D. Reid, “Experimental criteria for steering and the einstein-podolsky-rosen paradox,” Phys. Rev. A 80, 032112 (2009).
[25] M. F. Pusey, “Negativity and steering: A stronger peres conjecture,” Phys. Rev. A 88, 032313 (2013).
[26] E. G. Cavalcanti, C. J. Foster, M. Fuwa, and H. M. Wiseman, “Analog of the clauser–horne–shimony–holt inequality for steering,” J. Opt. Soc. Am. B 32, A74 (2015).
[27] S. P. Walborn, A. Salles, R. M. Gomes, F. Toscano, and P. H. Souto Ribeiro, “Revealing hidden einstein-podolsky-rosen nonlocality,” Phys. Rev. Lett. 106, 130402 (2011).
[28] J. Schneeloch, C. J. Broadbent, S. P. Walborn, E. G. Cavalcanti, and J. C. Howell,“Einstein-podolsky-rosen steering inequalities from entropic uncertainty relations,”Phys. Rev. A 87, 062103 (2013).
[29] T. Pramanik, M. Kaplan, and A. S. Majumdar, “Fine-grained einstein-podolskyrosen–steering inequalities,” Phys. Rev. A 90, 050305 (2014).
[30] I. Kogias, P. Skrzypczyk, D. Cavalcanti, A. Acín, and G. Adesso, “Hierarchy of steering criteria based on moments for all bipartite quantum systems,” Phys. Rev. Lett. 115, 210401 (2015).
[31] H. C. Nguyen and T. Vu, “Necessary and sufficient condition for steerability of twoqubit states by the geometry of steering outcomes,” Europhysics Letters 115, 10003 (2016).
[32] L. Vandenberghe and S. Boyd, “Semidefinite programming,” SIAM Review 38, 49 (1996), https://doi.org/10.1137/1038003.
[33] S. Lu, S. Huang, K. Li, J. Li, J. Chen, D. Lu, Z. Ji, Y. Shen, D. Zhou, and B. Zeng,“Separability-entanglement classifier via machine learning,” Phys. Rev. A 98, 012315 (2018).
[34] A. Canabarro, S. Brito, and R. Chaves, “Machine learning nonlocal correlations,”Phys. Rev. Lett. 122, 200401 (2019).
[35] D.-L. Deng, “Machine learning detection of bell nonlocality in quantum many-body systems,” Phys. Rev. Lett. 120, 240402 (2018).
[36] M. Neugebauer, L. Fischer, A. Jäger, S. Czischek, S. Jochim, M. Weidemüller, and M. Gärttner, “Neural-network quantum state tomography in a two-qubit experiment,” Phys. Rev. A 102, 042604 (2020).
[37] Y.-Q. Zhang, L.-J. Yang, Q.-L. He, and L. Chen, “Machine learning on quantifying quantum steerability,” Quantum Information Processing 19, 1 (2020).
[38] Y.-C. Ma and M.-H. Yung, “Transforming bell’s inequalities into state classifiers with machine learning,” npj Quantum Information 4, 34 (2018).
[39] C. Ren and C. Chen, “Steerability detection of an arbitrary two-qubit state via machine learning,” Phys. Rev. A 100, 022314 (2019).
[40] P. Skrzypczyk, M. Navascués, and D. Cavalcanti, “Quantifying einstein-podolskyrosen steering,” Phys. Rev. Lett. 112, 180404 (2014).
[41] J. Bowles, F. Hirsch, M. T. Quintino, and N. Brunner, “Sufficient criterion for guaranteeing that a two-qubit state is unsteerable,” Phys. Rev. A 93, 022121 (2016).
[42] A. Milne, D. Jennings, S. Jevtic, and T. Rudolph, “Quantum correlations of twoqubit states with one maximally mixed marginal,” Phys. Rev. A 90, 024302 (2014).
[43] D. Li, X. Li, H. Huang, and X. Li, “Stochastic local operations and classical communication invariant and the residual entanglement for n qubits,” Phys. Rev. A 76, 032304 (2007).
[44] S. Luo, “Quantum discord for two-qubit systems,” Phys. Rev. A 77, 042303 (2008).
[45] A. C. S. Costa and R. M. Angelo, “Quantification of einstein-podolsky-rosen steering for two-qubit states,” Phys. Rev. A 93, 020103 (2016).
[46] K. c. v. Jiráková, A. Černoch, K. Lemr, K. Bartkiewicz, and A. Miranowicz, “Experimental hierarchy and optimal robustness of quantum correlations of two-qubit states with controllable white noise,” Phys. Rev. A 104, 062436 (2021).
[47] A. Krogh, “What are artificial neural networks?” Nature biotechnology 26, 195 (2008).
[48] D. E. Rumelhart, G. E. Hinton, and R. J. Williams, “Learning representations by back-propagating errors,” nature 323, 533 (1986).
[49] N. Srivastava, G. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov,“Dropout: A simple way to prevent neural networks from overfitting,” J. Mach. Learn. Res. 15, 1929–1958 (2014).
[50] “Randomdensitymatrix of qetlab,” .
[51] S. Jevtic, M. Pusey, D. Jennings, and T. Rudolph, “Quantum steering ellipsoids,”Phys. Rev. Lett. 113, 020402 (2014).
[52] T. Rudolph and L. Catani, “Accessible information in a two-qubit system through the quantum steering ellipsoids formalism,” .
[53] M. W. Browne, “Cross-validation methods,” Journal of Mathematical Psychology 44, 108 (2000).