量子網路透過量子糾纏在多個空間分離的節點之間建立非古典關聯性，使得分散式量子資訊處理、量子通訊與量子感測等任務得以實現。然而，在實際的量子網路中，各節點的硬體元件不可避免地受到雜訊與不完美效應的影響，導致實際生成的量子態與理想目標態之間產生偏差；在極端情況下，部分節點甚至可能退化為僅能輸出既有古典資料的行為。此外，在多數分散式量子通訊協定中，網路參與者往往無法完全掌握其他節點的內部操作，使得整體網路必須在「不可信節點」的條件下加以評估。如何在此類實際且受限的情境中，可靠地判定量子網路是否仍保有非古典關聯性，成為量子網路發展中的一項核心問題。過去的研究多著重於在不可信節點條件下，透過網路保真度、糾纏見證或 Einstein–Podolsky–Rosen (EPR) 操控性見證、Bell–CHSH不等式等操作性準則，判定量子網路是否仍具非古典性。然而，這類方法通常提供的是「是否通過驗證」的判斷，較難描述實驗中非古典關聯性隨雜訊逐漸退化的連續行為，因此難以明確界定量子系統轉變為可由古典模型描述的臨界位置。基於此建立一個具有清楚物理意義、且能適用於不可信節點情境的定量框架，以描述量子–古典轉變過程之特性，具有重要的研究價值。

本論文提出一套新的理論與實驗框架，用以定量描述多節點量子網路中的非古典關聯性，並實驗性地展示量子–古典轉變。理論上，我們提出一種稱為「因果不連通量子–古典混合模型」的描述方式，在此架構下引入「互連性（interconnectivity）」作為量子關聯性的資源概念，進一步定義互連性組成量與互連性穩健量兩個量化指標，並證明其滿足資源理論所需的基本性質。基於上述理論框架，我們完成了以下三項主要的實驗的研究任務，首先，透過量子態斷層掃描重建二光子、三光子與四光子糾纏態，量化其互連性資源。其次，我們實驗展示了量子與古典間的轉變。為此，我們在實驗上製作一個可調變的 Werner 態，旨在透過變更噪音的強度結合本研究所提出量化的互連性組成量，來量化量子與古典之間的轉變過程。為了明確界定不同古典節點配置下的量子–古典邊界，我們針對每一種單一古典節點的位置配置分別進行討論。我們先以半正定規劃求得目標態的最佳古典擬態，再分解取得由不同 Greenberger–Horne–Zeilinger 基底態所構成的噪音分量及其權重。以實驗重建態為基礎，經由理論局域么正操作生成由實際實驗態衍生之古典擬態噪音。接著，我們以狀態純度作為混合參數，透過逐步降低純度，將內部組成固定的古典擬態噪音混入實驗重建態中，形成不同噪音強度下的 Werner 態。透過量化互連性組成量在不同純度下的動態變化，我們藉由其隨純度下降而歸零的臨界點，辨識出不同古典節點配置下的量子–古典邊界。最後，我們將上述的框架應用於不可信裝置情境，提出並實作一套多邊裝置無關的量子態斷層掃描（mSDI-QST）方案，使驗證者在不預設所有遠端量測裝置皆為可信的前提下，仍能判定斷層掃描所得之重建量子態是否可被視為可信，從而為實際量子網路中的狀態驗證與斷層掃描提供一種可實驗實現的方法。

Quantum networks establish nonclassical correlations among multiple spatially separated nodes through quantum entanglement, thereby enabling tasks such as distributed quantum information processing, quantum communication, and quantum sensing. In realistic quantum networks, however, the hardware components at each node inevitably suffer from noise and various imperfections, leading to deviations between the actually generated quantum states and the ideal target states. In extreme cases, some nodes may even degrade into devices that merely output pre-existing classical data. Moreover, in most distributed quantum communication protocols, network participants typically have limited knowledge of the internal operations performed by other nodes, such that the overall network must be evaluated under the assumption of untrusted nodes. How to reliably determine whether a quantum network still retains nonclassical correlations under such realistic and constrained conditions therefore constitutes a central challenge in the development of quantum networks. Previous studies have largely focused on assessing nonclassicality in the presence of untrusted nodes by employing operational criteria such as network fidelity, entanglement witnesses, or Einstein–Podolsky–Rosen (EPR) steering witnesses, Bell–CHSH inequalities. While these approaches are effective in certifying whether nonclassical correlations are present, they usually provide only a binary verdict of “violates” or “does not violate.” As a result, they are ill-suited for characterizing the continuous degradation of nonclassical correlations under increasing noise in experiments, and they do not offer a clear means to identify the critical point at which a quantum system becomes describable by a classical model. Consequently, it is of significant interest to establish a quantitative framework with clear physical meaning that remains applicable in scenarios involving untrusted nodes, in order to systematically characterize the quantum–classical transition.

In this thesis, we propose a new theoretical and experimental framework for the quantitative characterization of nonclassical correlations in multi-node quantum networks, and experimentally demonstrate the quantum–classical crossover. On the theoretical side, we introduce a descriptive framework termed the causally disconnected quantum–classical hybrid model. Within this framework, we formulate interconnectivity as a resource concept for quantum correlations, and further define two quantitative measures: the interconnectivity composition and the interconnectivity robustness. We prove that these measures satisfy the fundamental requirements of a resource theory. Based on the aforementioned theoretical framework, we have accomplished three primary experimental research tasks. First, employing a platform capable of generating six-photon polarization-entangled states as the testbed, we reconstruct two-photon, three-photon, and four-photon entangled states via quantum state tomography, subsequently quantifying their interconnectivity resources. Second, we experimentally demonstrate the quantum–classical crossover. To this end, we prepare a tunable Werner state in the experiment, aiming to quantify the quantum–classical crossover process by varying the noise intensity in conjunction with the quantified interconnectivity composition proposed in this study. To explicitly delineate the quantum–classical boundary under different classical-node configurations, we consider each single-classical-node position setting separately. Within the hybrid model, we first use semidefinite programming to obtain the optimal classical mimicry of the target state. By decomposing this optimal mimicry, we extract the noise components—constructed from different Greenberger–Horne–Zeilinger (GHZ) basis states—and their corresponding weights. Based on the experimentally reconstructed state, the classical-mimicry noise derived from the actual experimental state is then generated via theoretical local unitary transformations. Next, we take the state purity as the mixing parameter and, by progressively lowering the purity, mix into the experimentally reconstructed state the classical-mimicry noise whose internal composition remains fixed, thereby forming Werner states under varying noise intensities. By quantifying the dynamic evolution of the interconnectivity composition across different purities, we identify the critical point at which it vanishes as the purity decreases, thereby identifying the quantum–classical boundary for each classical-node configuration. Finally, we extend the above framework to scenarios involving untrusted devices by proposing and experimentally implementing a multi-sided device-independent quantum state tomography scheme. This scheme allows a verifier to assess whether the reconstructed quantum state obtained from tomography can be regarded as reliable, without the prerequisite assumption that all remote measurement devices are trustworthy, thereby providing an experimentally implementable method for state verification and tomography in practical quantum networks.

[1] H. J. Kimble, “The quantum internet,” Nature, vol. 453, pp. 1023–1030, 2008.
[2] S. Ritter, C. Nölleke, C. Hahn, A. Reiserer, A. Neuzner, M. Uphoff, M. Mücke, E. Figueroa, J. Bochmann, and G. Rempe, “An elementary quantum network of single atoms in optical cavities,” Nature, vol. 484, no. 7393, pp. 195–200, 2012.
[3] S. Wehner, D. Elkouss, and R. Hanson, “Quantum internet: A vision for the road ahead,” Science, vol. 362, no. 6412, p. eaam9288, 2018.
[4] M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Physical Review A, vol. 59, p. 1829, 1999.
[5] Y.-A. Chen, A.-N. Zhang, Z. Zhao, X.-Q. Zhou, C.-Y. Lu, C.-Z. Peng, T. Yang, and J.-W. Pan, “Experimental quantum secret sharing and third-man quantum cryptography,” Physical review letters, vol. 95, no. 20, p. 200502, 2005.
[6] D. Markham and B. C. Sanders, “Graph states for quantum secret sharing,” Physical Review A—Atomic, Molecular, and Optical Physics, vol. 78, no. 4, p. 042309, 2008.
[7] B. Bell, D. Markham, D. Herrera-Martí, A. Marin, W. Wadsworth, J. Rarity, and M. Tame, “Experimental demonstration of graph-state quantum secret sharing,” Nature communications, vol. 5, no. 1, pp. 1–12, 2014.
[8] H. Lu, Z. Zhang, L.-K. Chen, Z.-D. Li, C. Liu, L. Li, N.-L. Liu, X. Ma, Y.-A. Chen, and J.-W. Pan, “Secret sharing of a quantum state,” Physical review letters, vol. 117, no. 3, p. 030501, 2016.
[9] P. Komar, E. M. Kessler, M. Bishof, L. Jiang, A. S. Sørensen, J. Ye, and M. D. Lukin, “A quantum network of clocks,” Nature Physics, vol. 10, no. 8, pp. 582–587, 2014.
[10] T. J. Proctor, P. A. Knott, and J. A. Dunningham, “Multiparameter estimation in networked quantum sensors,” Physical review letters, vol. 120, no. 8, p. 080501, 2018.
[11] R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Physical review letters, vol. 86, p. 5188, 2001.
[12] P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature, vol. 434, pp. 169–176, 2005.
[13] A. Broadbent, J. Fitzsimons, and E. Kashefi, “Universal blind quantum computation,” pp. 517–526, 2009.
[14] S. Barz, E. Kashefi, A. Broadbent, J. F. Fitzsimons, A. Zeilinger, and P. Walther, “Demonstration of blind quantum computing,” science, vol. 335, no. 6066, pp. 303– 308, 2012.
[15] K. Chen and H.-K. Lo, “Multi-partite quantum cryptographic protocols with noisy ghz states,” arXiv preprint quant-ph/0404133, 2004.
[16] H.-K. Lo, M. Curty, and K. Tamaki, “Secure quantum key distribution,” Nature Photonics, vol. 8, no. 8, pp. 595–604, 2014.
[17] M. Epping, H. Kampermann, D. Bruß, et al., “Multi-partite entanglement can speed up quantum key distribution in networks,” New Journal of Physics, vol. 19, no. 9, p. 093012, 2017.
[18] C.-M. Li, K. Chen, Y.-N. Chen, Q. Zhang, Y.-A. Chen, and J.-W. Pan, “Genuine highorder einstein-podolsky-rosen steering,” Physical review letters, vol. 115, p. 010402, 2015.
[19] C.-Y. Huang, N. Lambert, C.-M. Li, Y.-T. Lu, and F. Nori, “Securing quantum networking tasks with multipartite einstein-podolsky-rosen steering,” Physical Review A, vol. 99, no. 1, p. 012302, 2019.
[20] H. Lu, C.-Y. Huang, Z.-D. Li, X.-F. Yin, R. Zhang, T.-L. Liao, Y.-A. Chen, C.-M. Li, and J.-W. Pan, “Counting classical nodes in quantum networks,” Physical review letters, vol. 124, no. 18, p. 180503, 2020.
[21] W.-T. Kao, C.-Y. Huang, T.-J. Tsai, S.-H. Chen, S.-Y. Sun, Y.-C. Li, T.-L. Liao, C.-S. Chuu, H. Lu, and C.-M. Li, “Scalable determination of multipartite entanglement in quantum networks,” npj Quantum Information, vol. 10, no. 1, p. 73, 2024.
[22] D. Mayers and A. Yao, “Self testing quantum apparatus,” arXiv preprint quantph/ 0307205, 2003.
[23] D. Mayers and A. Yao, “Quantum cryptography with imperfect apparatus,” in Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No. 98CB36280), pp. 503–509, IEEE, 1998.
[24] Y.-Q. Nie, J.-Y. Guan, H. Zhou, Q. Zhang, X. Ma, J. Zhang, and J.-W. Pan, “Experimentalmeasurement-device-independent quantum random-number generation,” Physical Review A, vol. 94, no. 6, p. 060301, 2016.
[25] S. Pironio, A. Acín, S. Massar, A. B. de La Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, et al., “Random numbers certified by bell＇s theorem,” Nature, vol. 464, no. 7291, pp. 1021–1024, 2010.
[26] Y. Liu, Q. Zhao, M.-H. Li, J.-Y. Guan, Y. Zhang, B. Bai, W. Zhang, W.-Z. Liu, C. Wu, X. Yuan, et al., “Device-independent quantum random-number generation,” Nature, vol. 562, no. 7728, pp. 548–551, 2018.
[27] H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Physical review letters, vol. 108, no. 13, p. 130503, 2012.
[28] U. Vazirani and T. Vidick, “Fully device independent quantum key distribution,” Communications of the ACM, vol. 62, no. 4, pp. 133–133, 2019.
[29] M. Pawłowski and N. Brunner, “Semi-device-independent security of one-way quantum key distribution,” Physical Review A, vol. 84, p. 010302, 2011.
[30] A. Gheorghiu, E. Kashefi, and P. Wallden, “Robustness and device independence of verifiable blind quantum computing,” New Journal of Physics, vol. 17, no. 8, p. 083040, 2015.
[31] M. Hajdušek, C. A. Pérez-Delgado, and J. F. Fitzsimons, “Device-independent verifiable blind quantum computation,” arXiv preprint arXiv:1502.02563, 2015.
[32] J. F. Fitzsimons and E. Kashefi, “Unconditionally verifiable blind quantum computation,” Physical Review A, vol. 96, no. 1, p. 012303, 2017.
[33] D. Wu, Q. Zhao, C. Wang, L. Huang, Y.-F. Jiang, B. Bai, Y. Zhou, X.-M. Gu, F.-M. Liu, Y.-Q. Mao, et al., “Closing the locality and detection loopholes in multiparticle entanglement self-testing,” Physical Review Letters, vol. 128, no. 25, p. 250401, 2022.
[34] F. Baccari, R. Augusiak, I. Šupić, J. Tura, and A. Acín, “Scalable bell inequalities for qubit graph states and robust self-testing,” Physical review letters, vol. 124, no. 2, p. 020402, 2020.
[35] J. Kaniewski, “Analytic and nearly optimal self-testing bounds for the clauser-horneshimony- holt and mermin inequalities,” Physical review letters, vol. 117, no. 7, p. 070402, 2016.
[36] Q. Zhao and Y. Zhou, “Constructing multipartite bell inequalities from stabilizers,” Physical Review Research, vol. 4, no. 4, p. 043215, 2022.
[37] H.-W. Li, M. Pawłowski, Z.-Q. Yin, G.-C. Guo, and Z.-F. Han, “Semi-deviceindependent randomness certification using n→ 1 quantum random access codes,” Physical Review A—Atomic, Molecular, and Optical Physics, vol. 85, no. 5, p. 052308, 2012.
[38] H.-W. Li, Z.-Q. Yin, Y.-C. Wu, X.-B. Zou, S. Wang, W. Chen, G.-C. Guo, and Z.- F. Han, “Semi-device-independent random-number expansion without entanglement,” Physical Review A—Atomic, Molecular, and Optical Physics, vol. 84, no. 3, p. 034301, 2011.
[39] Y.-C. Liang, T. Vértesi, and N. Brunner, “Semi-device-independent bounds on entanglement,” Physical Review A—Atomic, Moleculavsupic2020selfr, and Optical Physics, vol. 83, no. 2, p. 022108, 2011.
[40] C. Branciard, E. G. Cavalcanti, S. P. Walborn, V. Scarani, and H. M. Wiseman, “Onesided device-independent quantum key distribution: Security, feasibility, and the connection with steering,” Physical Review A—Atomic, Molecular, and Optical Physics, vol. 85, no. 1, p. 010301, 2012.
[41] N. Walk, S. Hosseini, J. Geng, O. Thearle, J. Y. Haw, S. Armstrong, S. M. Assad, J. Janousek, T. C. Ralph, T. Symul, et al., “Experimental demonstration of gaussian protocols for one-sided device-independent quantum key distribution,” Optica, vol. 3, no. 6, pp. 634–642, 2016.
[42] C. Jebaratnam, D. Das, A. Roy, A. Mukherjee, S. S. Bhattacharya, B. Bhattacharya, A. Riccardi, and D. Sarkar, “Tripartite-entanglement detection through tripartite quan- um steering in one-sided and two-sided device-independent scenarios,” Physical Review A, vol. 98, no. 2, p. 022101, 2018.
[43] T. H. Yang, T. Vértesi, J.-D. Bancal, V. Scarani, and M. Navascués, “Robust and versatile black-box certification of quantum devices,” Phys. Rev. Lett., vol. 113, p. 040401, July 2014.
[44] K. F. Pál, T. Vértesi, and M. Navascués, “Device-independent tomography of multipartite quantum states,” Phys. Rev. A, vol. 90, no. 4, p. 042340, 2014.
[45] A. Gočanin, I. Šupić, and B. Dakić, “Sample-efficient device-independent quantum state verification and certification,” PRX Quantum, vol. 3, no. 1, p. 010317, 2022.
[46] K.-S. Chen, G. N. M. Tabia, C. Jebarathinam, S. Mal, J.-Y. Wu, and Y.-C. Liang, “Quantum correlations on the no-signaling boundary: self-testing and more,” Quantum, vol. 7, p. 1054, 2023.
[47] I. Šupić and J. Bowles, “Self-testing of quantum systems: a review,” Quantum, vol. 4, p. 337, 2020.
[48] D. Mogilevtsev, J. Řeháček, and Z. Hradil, “Self-calibration for self-consistent tomography,” New Journal of Physics, vol. 14, no. 9, p. 095001, 2012.
[49] J. Y. Sim, J. Shang, H. K. Ng, and B.-G. Englert, “Proper error bars for self-calibrating quantum tomography,” Physical Review A, vol. 100, no. 2, p. 022333, 2019.
[50] A. M. Brańczyk, D. H. Mahler, L. A. Rozema, A. Darabi, A. M. Steinberg, and D. F. James, “Self-calibrating quantum state tomography,” New Journal of Physics, vol. 14, no. 8, p. 085003, 2012.
[51] C. Stark, “Self-consistent tomography of the state-measurement gram matrix,” Physical Review A, vol. 89, no. 5, p. 052109, 2014.
[52] P. Cerfontaine, R. Otten, and H. Bluhm, “Self-consistent calibration of quantum-gate sets,” Physical Review Applied, vol. 13, no. 4, p. 044071, 2020.
[53] I. Roth, J. Wilkens, D. Hangleiter, and J. Eisert, “Semi-device-dependent blind quantum tomography,” Quantum, vol. 7, p. 1053, 2023.
[54] M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information. Cambridge university press, 2010.
[55] E. Schrödinger, “Discussion of probability relations between separated systems,” in Mathematical Proceedings of the Cambridge Philosophical Society, vol. 31, pp. 555– 563, Cambridge University Press, 1935.
[56] H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, entanglement, nonlocality, and the einstein-podolsky-rosen paradox,” Physical Review Letters, vol. 98, no. 14, p. 140402, 2007.
[57] R. Uola, A. C. Costa, H. C. Nguyen, and O. Gühne, “Quantum steering,” Reviews of Modern Physics, vol. 92, no. 1, p. 015001, 2020.
[58] J. S. Bell, “On the einstein-podolsky-rosen paradox,” Physics Physique Fizika, vol. 1, no. 3, p. 195, 1964.
[59] J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Physical Review Letters, vol. 23, no. 15, p. 880, 1969.
[60] N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Bell nonlocality,” Reviews of Modern Physics, vol. 86, no. 2, p. 419, 2014.
[61] A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?,” Physical Review, vol. 47, no. 10, p. 777, 1935.
[62] M. Piani and J. Watrous, “Necessary and sufficient quantum information characterization of einstein-podolsky-rosen steering,” Physical Review Letters, vol. 114, no. 6, p. 060404, 2015.
[63] N. Gisin and B. Gisin, “A local hidden variable model of quantum correlation exploiting the detection loophole,” Physics Letters A, vol. 260, no. 5, pp. 323–327, 1999.
[64] B. F. Toner and D. Bacon, “Communication cost of simulating bell correlations,” Physical Review Letters, vol. 91, no. 18, p. 187904, 2003.
[65] S. Pironio, “Violations of bell inequalities as lower bounds on the communication cost of nonlocal correlations,” Physical Review A, vol. 68, no. 6, p. 062102, 2003.
[66] A. Montina and S. Wolf, “Information-based measure of nonlocality,” New Journal of Physics, vol. 18, no. 1, p. 013035, 2016.
[67] M. Steiner, “Towards quantifying non-local information transfer: finite-bit nonlocality,”Physics Letters A, vol. 270, no. 5, pp. 239–244, 2000.
[68] C. Branciard and N. Gisin, “Quantifying the nonlocality of greenberger-hornezeilinger quantum correlations by a bounded communication simulation protocol,” Physical Review Letters, vol. 107, no. 2, p. 020401, 2011.
[69] W. Van Dam, R. D. Gill, and P. D. Grunwald, “The statistics retained of highdimensional proofs,” IEEE Transactions on Information Theory, 2003.
[70] A. Acín, R. D. Gill, and N. Gisin, “Optimal bell tests do not require maximally entangled states,” Physical Review Letters, vol. 95, no. 21, p. 210402, 2005.
[71] M. Junge, C. Palazuelos, D. Pérez-García, I. Villanueva, and M. M. Wolf, “Operator space theory: a natural framework for bell inequalities,” Physical Review Letters, vol. 104, no. 17, p. 170405, 2010.
[72] S. G. D. A. Brito, B. Amaral, and R. Chaves, “Quantifying bell nonlocality with the trace distance,” Physical Review A, vol. 97, no. 2, p. 022111, 2018.
[73] D. Kaszlikowski, P. Gnaciński, M. Żukowski, W. Miklaszewski, and A. Zeilinger, “Violations of local realism by two entangled n-dimensional systems are stronger than for two qubits,” Physical Review Letters, vol. 85, no. 21, p. 4418, 2000.
[74] A. Acin, T. Durt, N. Gisin, and J. I. Latorre, “Quantum nonlocality in two three-level systems,” Physical Review A, vol. 65, no. 5, p. 052325, 2002.
[75] D. Pérez-García, M. M. Wolf, C. Palazuelos, I. Villanueva, and M. Junge, “Unbounded violation of tripartite bell inequalities,” Communications in Mathematical Physics, vol. 279, pp. 455–486, 2008.
[76] S. Massar, “Nonlocality, closing the detection loophole, and communication complexity,” Physical Review A, vol. 65, no. 3, p. 032112, 2002.
[77] P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Physical Review Letters, vol. 75, p. 4337, 1995.
[78] C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, “Generation of correlated photon pairs in type-ii parametric down conversion—revisited,” Journal of Modern Optics, vol. 48, pp. 1997–2007, 2001.
[79] Y. Shih, “Entangled biphoton source-property and preparation,” Reports on Progress in Physics, vol. 66, p. 1009, 2003.
[80] J.-H. Hsieh, “Theory of quantifying quantum-mechanical process and its application,” National Cheng Kung University, 2017.
[81] C.-K. Hong, Z.-Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Physical review letters, vol. 59, p. 2044, 1987.
[82] J.-w. Pan and A. Zeilinger, “Greenberger-horne-zeilinger-state analyzer,” Physical Review A, vol. 57, p. 2208, 1998.
[83] J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski,“Multiphoton entanglement and interferometry,” Reviews of Modern Physics, vol. 84, p. 777, 2012.
[84] D.-G. Im, Y. Kim, and Y.-H. Kim, “Dispersion cancellation in a quantum interferometer with independent single photons,” Optics Express, vol. 29, pp. 2348–2363, 2021.
[85] U. Q. Devices, “Logic-16 https://uqdevices.com/products/,”
[86] S.-Y. Sun, “Experimental capability of photon interference for generating six-photon entanglement,” Master’s thesis, National Cheng Kung University, 2023.
[87] L. Yu-Cheng, “Efficient experimental detection of quantum coherence transmission in a six-photon quantum network.,” Master’s thesis, National Cheng Kung University, 2023.
[88] Z. Zhao, T. Yang, Y.-A. Chen, A.-N. Zhang, M. Żukowski, and J.-W. Pan, “Experimental violation of local realism by four-photon greenberger-horne-zeilinger entanglement,”Physical review letters, vol. 91, p. 180401, 2003.
[89] D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell＇s theorem without inequalities,” American Journal of Physics, vol. 58, no. 12, pp. 1131–1143, 1990.
[90] O. Gühne, C.-Y. Lu, W.-B. Gao, and J.-W. Pan, “Toolbox for entanglement detection and fidelity estimation,” Physical Review A, vol. 76, p. 030305, 2007.
[91] W.-T. Kao, C.-Y. Huang, T.-J. Tsai, S.-H. Chen, S.-Y. Sun, Y.-C. Li, T.-L. Liao, C.-S.Chuu, H. Lu, and C.-M. Li, “Scalable quantum network determination with einsteinpodolsky-rosen steering,” arXiv preprint arXiv:2303.17771, 2023.
[92] M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Physical review letters, vol. 92, p. 087902, 2004.
[93] G. Tóth and O. Gühne, “Detecting genuine multipartite entanglement with two local measurements,” Physical review letters, vol. 94, no. 6, p. 060501, 2005.
[94] I. Thorlabs, “Fiber polarization beam splitter / combiner — product page.”
[95] I. Thorlabs, “Motorized fiber polarization controller — product page.”
[96] N. D. Mermin, “Hidden variables and the two theorems of john bell,” Reviews of Modern Physics, vol. 65, no. 3, p. 803, 1993.
[97] O. Gühne, G. Tóth, P. Hyllus, and H. J. Briegel, “Bell inequalities for graph states,” Physical review letters, vol. 95, no. 12, p. 120405, 2005.
[98] J.-Å. Larsson, “Loopholes in bell inequality tests of local realism,” Journal of Physics A: Mathematical and Theoretical, vol. 47, no. 42, p. 424003, 2014.
[99] D. F. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Physical Review A, vol. 64, no. 5, p. 052312, 2001.
[100] J. L. O’Brien, G. J. Pryde, A. Gilchrist, D. F. James, N. K. Langford, T. C. Ralph, and A. G. White, “Quantum process tomography of a controlled-not gate,” Physical review letters, vol. 93, no. 8, p. 080502, 2004.
[101] Y.-Q. Nie, H. Zhou, J.-Y. Guan, Q. Zhang, X. Ma, J. Zhang, and J.-W. Pan, “Quantum coherence witness with untrusted measurement devices,” Physical Review Letters, vol. 123, no. 9, p. 090502, 2019.
[102] Y.-H. Kim, S. P. Kulik, M. V. Chekhova, W. P. Grice, and Y. Shih, “Experimental entanglement concentration and universal bell-state synthesizer,” Physical Review A, vol. 67, p. 010301, 2003.
[103] X.-L. Wang, L.-K. Chen, W. Li, H.-L. Huang, C. Liu, C. Chen, Y.-H. Luo, Z.-E. Su, D. Wu, Z.-D. Li, et al., “Experimental ten-photon entanglement,” Physical review letters, vol. 117, p. 210502, 2016.
[104] H.-S. Zhong, Y. Li, W. Li, L.-C. Peng, Z.-E. Su, Y. Hu, Y.-M. He, X. Ding, W. Zhang, H. Li, et al., “12-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion,” Physical review letters, vol. 121, p. 250505, 2018.
[105] L.-K. Chen, Z.-D. Li, X.-C. Yao, M. Huang, W. Li, H. Lu, X. Yuan, Y.-B. Zhang,X. Jiang, C.-Z. Peng, et al., “Observation of ten-photon entanglement using thin bib 3 o 6 crystals,” Optica, vol. 4, pp. 77–83, 2017.
[106] C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu,T. Johnston, Y. Bromberg, L. Caspani, et al., “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science, vol. 351, pp. 1176–1180, 2016.
[107] E. Chitambar and G. Gour, “Quantum resource theories,” Reviews of modern physics,vol. 91, p. 025001, 2019.
[108] D. Cavalcanti and P. Skrzypczyk, “Quantum steering: a review with focus on semidefinite programming,” Reports on Progress in Physics, vol. 80, no. 2, p. 024001, 2016.
[109] J. Löfberg, “Yalmip: A toolbox for modeling and optimization in matlab,” pp. 284–289, 2004.
[110] K.-C. Toh, M. J. Todd, and R. H. Tütüncü, “Sdpt3—a matlab software package for semidefinite programming, version 1.3,” Optimization methods and software, vol. 11,pp. 545–581, 1999.