447 lines
13 KiB
BibTeX
447 lines
13 KiB
BibTeX
@article{aschauer,
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author = {Aschauer, Hans and Calsamiglia, John and Hein, M. and Briegel, Hans J.},
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title = {Local invariants for multi-partite entangled states allowing for a simple entanglement criterion},
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journal = {Quantum Information and Computation},
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volume = {4},
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number = {5},
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pages = {383--395},
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year = {2004},
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doi = {10.26421/QIC4.5-4}
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}
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@article{peres,
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author = {Peres, Asher},
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title = {Separability Criterion for Density Matrices},
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journal = {Physical Review Letters},
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volume = {77},
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number = {8},
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pages = {1413--1415},
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year = {1996},
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doi = {10.1103/PhysRevLett.77.1413}
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}
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@article{horodeckiPPT,
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author = {Horodecki, Micha{\l} and Horodecki, Pawe{\l} and Horodecki, Ryszard},
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title = {Separability of mixed states: necessary and sufficient conditions},
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journal = {Physics Letters A},
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volume = {223},
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number = {1--2},
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pages = {1--8},
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year = {1996},
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doi = {10.1016/S0375-9601(96)00706-2}
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}
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@article{bennettUPB,
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author = {Bennett, Charles H. and DiVincenzo, David P. and Mor, Tal and Shor, Peter W. and Smolin, John A. and Terhal, Barbara M.},
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title = {Unextendible Product Bases and Bound Entanglement},
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journal = {Physical Review Letters},
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volume = {82},
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number = {26},
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pages = {5385--5388},
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year = {1999},
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doi = {10.1103/PhysRevLett.82.5385}
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}
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@article{chenwu,
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author = {Chen, Kai and Wu, Ling-An},
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title = {A matrix realignment method for recognizing entanglement},
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journal = {Quantum Information and Computation},
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volume = {3},
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number = {3},
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pages = {193--202},
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year = {2003}
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}
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@article{devicente,
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author = {de Vicente, Julio I.},
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title = {Separability criteria based on the Bloch representation of density matrices},
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journal = {Quantum Information and Computation},
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volume = {7},
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number = {7},
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pages = {624--638},
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year = {2007}
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}
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@article{hassanjoag,
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author = {Hassan, Ali S. M. and Joag, Pramod S.},
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title = {Separability criterion for multipartite quantum states based on the Bloch representation of density matrices},
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journal = {Quantum Information and Computation},
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volume = {8},
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number = {8},
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pages = {773--790},
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year = {2008}
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}
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@article{devicentehuber,
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author = {de Vicente, Julio I. and Huber, Marcus},
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title = {Multipartite entanglement detection from correlation tensors},
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journal = {Physical Review A},
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volume = {84},
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number = {6},
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pages = {062306},
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year = {2011},
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doi = {10.1103/PhysRevA.84.062306}
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}
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@article{laskowski2011,
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author = {Laskowski, Wieslaw and Markiewicz, Marcin and Paterek, Tomasz and {\v{Z}}ukowski, Marek},
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title = {Correlation-tensor criteria for genuine multiqubit entanglement},
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journal = {Physical Review A},
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volume = {84},
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number = {6},
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pages = {062305},
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year = {2011},
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doi = {10.1103/PhysRevA.84.062305}
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}
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@article{klocklhuber2015,
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author = {Kl{\"o}ckl, Claude and Huber, Marcus},
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title = {Characterizing multipartite entanglement without shared reference frames},
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journal = {Physical Review A},
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volume = {91},
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number = {4},
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pages = {042339},
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year = {2015},
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doi = {10.1103/PhysRevA.91.042339}
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}
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@article{li2014,
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author = {Li, Ming and Wang, Jing and Fei, Shao-Ming and Li-Jost, Xianqing},
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title = {Quantum separability criteria for arbitrary-dimensional multipartite states},
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journal = {Physical Review A},
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volume = {89},
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number = {2},
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pages = {022325},
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year = {2014},
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doi = {10.1103/PhysRevA.89.022325}
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}
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@article{shen2016,
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author = {Shen, Shu-Qian and Yu, Juan and Li, Ming and Fei, Shao-Ming},
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title = {Improved Separability Criteria Based on Bloch Representation of Density Matrices},
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journal = {Scientific Reports},
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volume = {6},
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pages = {28850},
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year = {2016},
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doi = {10.1038/srep28850}
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}
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@article{sarbicki2020,
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author = {Sarbicki, Gniewomir and Scala, Giovanni and Chru{\'s}ci{\'n}ski, Dariusz},
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title = {Family of multipartite separability criteria based on a correlation tensor},
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journal = {Physical Review A},
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volume = {101},
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number = {1},
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pages = {012341},
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year = {2020},
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doi = {10.1103/PhysRevA.101.012341}
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}
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@article{zhao2020,
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author = {Zhao, Hui and Zhang, Mei-Ming and Jing, NaiHuan and Wang, Zhi-Xi},
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title = {Separability criteria based on Bloch representation of density matrices},
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journal = {Quantum Information Processing},
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volume = {19},
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number = {1},
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year = {2020},
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doi = {10.1007/s11128-019-2504-2}
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}
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@misc{jingzhang2023,
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author = {Jing, Naihuan and Zhang, Mingming},
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title = {Criteria of genuine multipartite entanglement based on correlation tensors},
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year = {2023},
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eprint = {2301.06463},
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archivePrefix = {arXiv},
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primaryClass = {quant-ph},
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url = {https://arxiv.org/abs/2301.06463}
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}
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@misc{huang2024moments,
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author = {Huang, Xin and Jing, Naihuan},
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title = {Separability criteria based on the correlation tensor moments for arbitrary dimensional states},
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year = {2024},
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eprint = {2402.13162},
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archivePrefix = {arXiv},
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primaryClass = {quant-ph},
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url = {https://arxiv.org/abs/2402.13162}
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}
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@misc{huang2024extended,
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author = {Huang, Xin and Zhang, Tianyi and Jing, Naihuan},
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title = {A unifying separability criterion based on extended correlation tensor},
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year = {2024},
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eprint = {2406.17230},
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archivePrefix = {arXiv},
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primaryClass = {quant-ph},
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url = {https://arxiv.org/abs/2406.17230}
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}
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@misc{liyaoyangfei2025,
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author = {Li, Lei and Yao, Hongyang and Yang, Chao and Fei, Shao-Ming},
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title = {Separability criteria of quantum states based on generalized Bloch representation},
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year = {2025},
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eprint = {2510.24110},
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archivePrefix = {arXiv},
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primaryClass = {quant-ph},
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url = {https://arxiv.org/abs/2510.24110}
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}
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@article{vollbrechtwerner2001,
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author = {Vollbrecht, Karl Gerd H. and Werner, Reinhard F.},
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title = {Entanglement measures under symmetry},
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journal = {Physical Review A},
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volume = {64},
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number = {6},
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pages = {062307},
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year = {2001},
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doi = {10.1103/PhysRevA.64.062307}
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}
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@misc{fattal2004stabilizer,
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author = {Fattal, David and Cubitt, Toby S. and Yamamoto, Yoshihisa and Bravyi, Sergey and Chuang, Isaac L.},
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title = {Entanglement in the stabilizer formalism},
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year = {2004},
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eprint = {quant-ph/0406168},
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archivePrefix = {arXiv},
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primaryClass = {quant-ph},
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url = {https://arxiv.org/abs/quant-ph/0406168}
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}
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@article{heinEisertBriegel2004,
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author = {Hein, M. and Eisert, J. and Briegel, H. J.},
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title = {Multiparty entanglement in graph states},
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journal = {Physical Review A},
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volume = {69},
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number = {6},
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pages = {062311},
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year = {2004},
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doi = {10.1103/PhysRevA.69.062311}
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}
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@article{huangkuengpreskill2020,
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author = {Huang, Hsin-Yuan and Kueng, Richard and Preskill, John},
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title = {Predicting many properties of a quantum system from very few measurements},
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journal = {Nature Physics},
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volume = {16},
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number = {10},
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pages = {1050--1057},
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year = {2020},
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doi = {10.1038/s41567-020-0932-7}
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}
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@article{delathauwer,
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author = {De Lathauwer, Lieven and De Moor, Bart and Vandewalle, Joos},
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title = {A multilinear singular value decomposition},
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journal = {SIAM Journal on Matrix Analysis and Applications},
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volume = {21},
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number = {4},
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pages = {1253--1278},
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year = {2000},
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doi = {10.1137/S0895479896305696}
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}
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@misc{appleby2009,
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author = {Appleby, D. M.},
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title = {Properties of the extended Clifford group with applications to SIC-POVMs and MUBs},
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year = {2009},
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eprint = {0909.5233},
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archivePrefix = {arXiv},
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primaryClass = {quant-ph},
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doi = {10.48550/arXiv.0909.5233},
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url = {https://arxiv.org/abs/0909.5233}
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}
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@misc{applebyBengtssonChaturvedi2007,
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author = {Appleby, D. M. and Bengtsson, Ingemar and Chaturvedi, Subramanyan},
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title = {Spectra of phase point operators in odd prime dimensions and the extended Clifford group},
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year = {2007},
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eprint = {0710.3013},
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archivePrefix = {arXiv},
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primaryClass = {quant-ph},
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url = {https://arxiv.org/abs/0710.3013}
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}
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@article{vanDamHoward2011,
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author = {van Dam, Wim and Howard, Mark},
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title = {Bipartite entangled stabilizer mutually unbiased bases as maximum cliques of Cayley graphs},
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journal = {Physical Review A},
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volume = {84},
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number = {1},
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pages = {012117},
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year = {2011},
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doi = {10.1103/PhysRevA.84.012117}
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}
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@article{poppHiesmayr2024,
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author = {Popp, C. and Hiesmayr, B. C.},
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title = {Special features of the Weyl-Heisenberg Bell basis imply unusual entanglement structure of Bell-diagonal states},
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journal = {New Journal of Physics},
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volume = {26},
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number = {1},
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pages = {013039},
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year = {2024},
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doi = {10.1088/1367-2630/ad1f10}
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}
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@article{sutterPoppHiesmayr2026,
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author = {Sutter, T. C. and Popp, C. and Hiesmayr, B. C.},
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title = {Group-Theoretic Perspective on the {PPT} and Realignment Criteria in the Magic Simplex for Bipartite Qutrits},
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journal = {Physical Review A},
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volume = {113},
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number = {3},
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pages = {032440},
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year = {2026},
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doi = {10.1103/PhysRevA.113.032440}
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}
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@book{kato1995perturbation,
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author = {Kato, Tosio},
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title = {Perturbation Theory for Linear Operators},
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publisher = {Springer-Verlag},
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series = {Classics in Mathematics},
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year = {1995},
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note = {Reprint of the 1980 second edition}
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}
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@article{lewissendov2005,
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author = {Lewis, A. S. and Sendov, H. S.},
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title = {Nonsmooth analysis of singular values. {P}art {I}: Theory},
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journal = {Set-Valued Analysis},
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volume = {13},
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number = {3},
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pages = {213--241},
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year = {2005},
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doi = {10.1007/s11228-004-7197-7}
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}
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@article{zanardirasetti1997,
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author = {Zanardi, Paolo and Rasetti, Mario},
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title = {Noiseless Quantum Codes},
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journal = {Physical Review Letters},
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volume = {79},
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number = {17},
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pages = {3306--3309},
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year = {1997},
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doi = {10.1103/PhysRevLett.79.3306}
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}
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@article{kribslaflammepoulin2005,
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author = {Kribs, David and Laflamme, Raymond and Poulin, David},
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title = {Unified and Generalized Approach to Quantum Error Correction},
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journal = {Physical Review Letters},
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volume = {94},
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number = {18},
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pages = {180501},
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year = {2005},
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doi = {10.1103/PhysRevLett.94.180501}
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}
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@article{jungnitschmorodergühne2011,
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author = {Jungnitsch, Bastian and Moroder, Tobias and G{\"u}hne, Otfried},
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title = {Taming Multiparticle Entanglement},
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journal = {Physical Review Letters},
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volume = {106},
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number = {19},
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pages = {190502},
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year = {2011},
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doi = {10.1103/PhysRevLett.106.190502}
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}
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@article{guhneseevinck2010,
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author = {G{\"u}hne, Otfried and Seevinck, Michael},
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title = {Separability criteria for genuine multiparticle entanglement},
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journal = {New Journal of Physics},
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volume = {12},
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pages = {053002},
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year = {2010},
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doi = {10.1088/1367-2630/12/5/053002}
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}
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@article{novomorodergühne2013,
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author = {Novo, Leonardo and Moroder, Tobias and G{\"u}hne, Otfried},
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title = {Genuine multiparticle entanglement of permutationally invariant states},
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journal = {Physical Review A},
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volume = {88},
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pages = {012305},
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year = {2013},
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doi = {10.1103/PhysRevA.88.012305}
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}
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@article{jungnitschmorodergühne2011graphstates,
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author = {Jungnitsch, Bastian and Moroder, Tobias and G{\"u}hne, Otfried},
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title = {Entanglement Witnesses for Graph States: General Theory and Examples},
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journal = {Physical Review A},
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volume = {84},
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pages = {032310},
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year = {2011},
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doi = {10.1103/PhysRevA.84.032310}
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}
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@article{kampermannguhnewilmottbruss2012,
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author = {Kampermann, Hermann and G{\"u}hne, Otfried and Wilmott, Colin and Bru{\ss}, Dagmar},
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title = {Algorithm for characterizing stochastic local operations and classical communication classes of multiparticle entanglement},
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journal = {Physical Review A},
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volume = {86},
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pages = {032307},
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year = {2012},
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doi = {10.1103/PhysRevA.86.032307}
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}
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@article{higuchisudbery2000,
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author = {Higuchi, A. and Sudbery, A.},
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title = {How entangled can two couples get?},
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journal = {Physics Letters A},
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volume = {273},
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number = {4},
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pages = {213--217},
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year = {2000},
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doi = {10.1016/S0375-9601(00)00500-8}
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}
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@article{paraschivmiklinmorodergühne2018,
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author = {Paraschiv, Marius and Miklin, Nikolai and Moroder, Tobias and G{\"u}hne, Otfried},
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title = {Proving genuine multiparticle entanglement from separable nearest-neighbor marginals},
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journal = {Physical Review A},
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volume = {98},
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pages = {062102},
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year = {2018},
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doi = {10.1103/PhysRevA.98.062102}
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}
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@article{clivazhuberlamimurta2017,
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author = {Clivaz, Fabien and Huber, Marcus and Lami, Ludovico and Murta, Gl{\'a}ucia},
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title = {Genuine-multipartite entanglement criteria based on positive maps},
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journal = {Journal of Mathematical Physics},
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volume = {58},
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pages = {082201},
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year = {2017},
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doi = {10.1063/1.4998433},
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note = {arXiv:1609.08126}
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}
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@misc{weinbrennerricogoodenoughyugühne2026,
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author = {Weinbrenner, Lisa T. and Rico, Albert and Goodenough, Kenneth and Yu, Xiao-Dong and G{\"u}hne, Otfried},
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title = {Complete Hierarchies for the Geometric Measure of Entanglement},
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year = {2026},
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eprint = {2601.23243},
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archivePrefix = {arXiv},
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primaryClass = {quant-ph},
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note = {Very recent (Jan.\ 2026); addresses the geometric measure / overlap-with-product-states problem via multi-copy hierarchies, a related but distinct question from the correlation-tensor witness of Section~\ref{sec:gme-cluster-witness}. Check for overlap before submission.}
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}
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@misc{aschauer2026a,
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author = {Aschauer, Hans},
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title = {Symmetric Shadow Maps and Multipartite Correlation Criteria},
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year = {2026},
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note = {Unpublished}
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}
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@misc{aschauer2026b,
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author = {Aschauer, Hans},
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title = {Symmetry-adapted block decomposition of the shadow map},
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year = {2026},
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note = {Unpublished}
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}
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