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We construct the so-called generalized Choi states and show that it is distillable when it has negative partial transpose. We convert the distillability problem of 2-copy \n                  \n                    \n                  \n                  $$n\\times n$$\n                  \n                    \n                  \n                 Werner states into the determination of the positivity of an Hermitian matrix. We obtain several sufficient conditions by which the positivity holds. Further, we investigate the case \n                  \n                    \n                  \n                  $$n=3$$\n                  \n                    \n                  \n                 by the classification of \n                  \n                    \n                  \n                  $$2\\times 3\\times 3$$\n                  \n                    \n                  \n                 pure states.",{"EN":136},"Generalized Choi states and 2-distillability of quantum states",{"VOID":138},"[\"16342104346154038052\"]",{"VOID":140},"10.1007\u002Fs11128-018-1880-3","PUBLICATION","VERIFIED","2024-05-03T22:06:23.560+00:00","Auto 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P.: Separability criterion and inseparable mixed states with positive partial transposition. Phys. Lett. A 232, 333 (1997)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0375960197004167",{"doi":282},"10.1016\u002Fs0375-9601(97)00416-7",{"id":284,"text":285,"url":286,"identifiers":287},"4c68646b-0035-4279-8000-0006b275d4fa","DiVincenzo, D.P., Shor, P.W., Smolin, J.A., Terhal, B.M., Thapliyal, A.V.: Evidence for bound entangled states with negative partial transpose. Phys. Rev. A 61, 062312 (2000)","https:\u002F\u002Flink.springer.com\u002F10.1007\u002Fs10440-022-00541-7",{"doi":288},"10.1007\u002Fs10440-022-00541-7",{"id":284,"text":290,"url":286,"identifiers":291},"Shor, P.W., Smolin, J.A., Thapliyal, A.V.: Superactivation of bound entanglement. Phys. Rev. Lett. 90(10), 107901 (2003)",{"doi":288},{"id":284,"text":293,"url":286,"identifiers":294},"Tomiyama, J.: On the geometry of positive maps in matrix algebras. II. Linear Algebra Appl. 69, 169–177 (1985)",{"doi":288},{"id":284,"text":296,"url":286,"identifiers":297},"Horodecki, M., Horodecki, P.: Reduction criterion of separability and limits for a class of distillation protocols. Phys. Rev. A 59, 4206 (1999)",{"doi":288},{"id":284,"text":299,"url":286,"identifiers":300},"Terhal, B.M., Horodecki, P.: A schmidt number for density matrices. Phys. Rev. A 61, 040301 (2000)",{"doi":288},{"id":284,"text":302,"url":286,"identifiers":303},"Terhal, B.M., Horodecki, P., Smolin, J.A., Thapliyal, A.V.: Rank two bipartite bound entangled states do not exist. Theor. Comput. Sci. 292, 589–596 (2003)",{"doi":288},{"id":284,"text":305,"url":286,"identifiers":306},"Chen, L., Djokovic, D.Z.: Distillability and ppt entanglement of low-rank quantum states. J. Phys. A: Math. Theor. 44(28), 285303 (2011)",{"doi":288},{"id":284,"text":308,"url":286,"identifiers":309},"Chen, L., Djokovic, D.Z.: Distillability of non-positive-partial-transpose bipartite quantum states of rank four. Phys. Rev. A 94, 052318 (2016)",{"doi":288},{"id":284,"text":311,"url":286,"identifiers":312},"Hayashi, M., Chen, L.: Weaker entanglement between two parties guarantees stronger entanglement with a third party. Phys. Rev. A 84, 012325 (2011)",{"doi":288},{"id":18,"text":314,"url":18,"identifiers":315},"Chen, L., Hayashi, M.: Nondistillable entanglement guarantees distillable entanglement. Int. J. Mod. Phys. B 26(27n28), 1243008 (2012)",{},{"id":284,"text":317,"url":286,"identifiers":318},"Horodecki, M., Horodecki, P., Horodecki, R.: Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1–8 (1996)",{"doi":288},{"id":284,"text":320,"url":286,"identifiers":321},"Horodecki, M., Horodecki, P., Horodecki, R.: Mixed-state entanglement and distillation: is there a bound entanglement in nature? Phys. Rev. Lett. 80, 5239–5242 (1998)",{"doi":288},{"id":323,"text":324,"url":325,"identifiers":326},"dda03545-8da1-4786-8280-6adb261cea83","Werner, R.F.: Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277–4281 (1989)","https:\u002F\u002Flink.aps.org\u002Fdoi\u002F10.1103\u002FPhysRevA.40.4277",{"doi":327},"10.1103\u002Fphysreva.40.4277",{"id":329,"text":330,"url":331,"identifiers":332},"48b1e909-8181-4d86-bdca-85a8541a3d5e","Lin, M.: A completely PPT map. Linear Algebra Appl. 459, 404–410 (2014)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0024379514004911",{"doi":333},"10.1016\u002Fj.laa.2014.07.040",{"id":18,"text":335,"url":18,"identifiers":336},"Kye, S.-H.: Facial structures for various notions of positivity and applications to the theory of entanglement. Rev. Math. Phys. 25, 1330002 (2013)",{},{"id":284,"text":338,"url":286,"identifiers":339},"Cho, S.J., Kye, S.-H., Lee, S.G.: Generalized Choi maps in 3-dimensional matrix algebras. Linear Algebra Appl. 171, 213–224 (1992)",{"doi":288},{"id":284,"text":341,"url":286,"identifiers":342},"Choi, M.-D.: Positive linear maps on \\(C^*\\)-algebras. Canad. J. Math. 24, 520–529 (1972)",{"doi":288},{"id":284,"text":344,"url":286,"identifiers":345},"Marciniak, M.: On extremal positive maps acting between type I factors. Banach Center Publ. 89, 201–221 (2010)",{"doi":288},{"id":18,"text":347,"url":18,"identifiers":348},"Bernstein, D.S.: Matrix Mathematics: Theory, Facts, and Formulas, 2nd edn. Princeton University Press, Princeton (2009)",{},{"id":18,"text":350,"url":18,"identifiers":351},"Chen, L., Chen, Y.-X.: Range criterion and classification of true entanglement in a \\(2\\times M\\times N\\) system. Phys. Rev. A 73, 052310 (2006)",{},false,{"id":354,"createTime":355,"updateTime":356,"relativeEntities":357,"slug":358,"properties":359,"entityType":141,"verifyStatus":142,"verifyTime":370,"verifyNote":144,"languages":18,"translateLanguages":18,"viewCount":19,"primaryUrl":371,"fullTextUrl":18,"authors":372,"publicationType":204,"publisherRelationship":398,"citationCount":18,"citationInfo":18,"publishDate":463,"publishYear":272,"citationAnalyzeStatus":17,"lastCitationAnalyze":464,"indexDatabases":465,"openAccess":18,"references":18,"isForceReanalyzing":352},"6b05371d-b24b-48f2-815c-e2ea65778d51","2024-02-14T03:24:18.899+00:00","2026-07-22T16:35:40.247+00:00",[],"Any-entanglement-of-assistance-is-polygamous",{"abstract":360,"title":362,"gsPaper":364,"references":366,"doi":368},{"EN":361},"We propose a condition for a measure of quantum correlation to be polygamous without the traditional polygamy inequality. It is shown to be equivalent to the standard polygamy inequalities for any continuous measure of quantum correlation with the polygamy power. We then show that any entanglement of assistance is polygamous but not monogamous, and any faithful entanglement measure is not polygamous.",{"EN":363},"Any entanglement of assistance is polygamous",{"VOID":365},"[]",{"VOID":367},"Coffman, V., Kundu, J., Wootters, W.K.: Distributed entanglement. Phys. Rev. A 61, 052306 (2000)\nGour, G., Meyer, D.A., Sanders, B.C.: Deterministic entanglement of assistance and monogamy constraints. Phys. Rev. A 72, 042329 (2005)\nOsborne, T.J., Verstraete, F.: General monogamy inequality for bipartite qubit entanglement. Phys. Rev. Lett. 96, 220503 (2006)\nGour, G., Bandyopadhyay, S., Sanders, B.C.: Dual monogamy inequality for entanglement. J. Math. Phys. 48, 012108 (2007)\nOu, Y.C., Fan, H.: Monogamy inequality in terms of negativity for three-qubit states. Phys. Rev. A 75, 062308 (2007)\nZhu, X.N., Fei, S.M.: Entanglement monogamy relations of qubit systems. Phys. Rev. A 90, 024304 (2014)\nBai, Y.K., Xu, Y.F., Wang, Z.D.: General monogamy relation for the entanglement of formation in multiqubit systems. Phys. Rev. Lett. 113, 100503 (2014)\nChoi, J.H., Kim, J.S.: Negativity and strong monogamy of multiparty quantum entanglement beyond qubits. Phys. Rev. A 92, 042307 (2015)\nLuo, Y., Li, Y.: Monogamy of \\(\\alpha \\)th power entanglement measurement in qubit systems. Ann. Phys. 362, 511–520 (2015)\nKumar, A.: Conditions for monogamy of quantum correlations in multipartite systems. Phys. Lett. A 380, 3044–3050 (2016)\nKim, J.S., Das, A., Sanders, B.C.: Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extended negativity. Phys. Rev. A 79, 012329 (2009)\nBuscemi, F., Gour, G., Kim, J.S.: Polygamy of distributed entanglement. Phys. Rev. A 80, 012324 (2009)\nKim, J.S.: Polygamy of entanglement in multipartite quantum systems. Phys. Rev. A 80, 022302 (2009)\nLi, Z.G., Fei, S.M., Albeverio, S., Liu, W.M.: Bound of entanglement of assistance and monogamy constraints. Phys. Rev. A 80, 034301 (2009)\nStreltsov, A., Adesso, G., Piani, M., Bruß, D.: Are general quantum correlations monogamous? Phys. Rev. Lett. 109, 050503 (2012)\nKim, J.S.: General polygamy inequality of multiparty quantum entanglement. Phys. Rev. A 85, 062302 (2012)\nBraga, H.C., et al.: Monogamy of quantum discord by multipartite correlations. Phys. Rev. A 86, 062106 (2012)\nLiu, S.Y., Li, B., Yang, W.L., Fan, H.: Monogamy deficit for quantum correlations in a multipartite quantum system. Phys. Rev. A 87, 062120 (2013)\nReid, M.D.: Monogamy inequalities for the Einstein–Podolsky–Rosen paradox and quantum steering. Phys. Rev. A 88, 062108 (2013)\nde Oliveira, T.R., Cornelio, M.F., Fanchini, F.F.: Monogamy of entanglement of formation. Phys. Rev. A 89, 034303 (2014)\nRegula, B., DiMartino, S., Lee, S., Adesso, G.: Strong monogamy conjecture for multiqubit entanglement: the four-qubit case. Phys. Rev. Lett. 113, 110501 (2014)\nEltschka, C., Siewert, J.: Monogamy equalities for qubit entanglement from Lorentz invariance. Phys. Rev. Lett. 114, 140402 (2015)\nZhu, X.N., Fei, S.M.: Entanglement monogamy relations of concurrence for \\(N\\)-qubit systems. Phys. Rev. A 92, 062345 (2015)\nLancien, C., et al.: Should entanglement measures be monogamous or faithful? Phys. Rev. Lett. 117, 060501 (2016)\nLami, L., Hirche, C., Adesso, G., Winter, A.: Schur complement inequalities for covariance matrices and monogamy of quantum correlations. Phys. Rev. Lett. 117, 220502 (2016)\nSong, W., et al.: General monogamy relation of multiqubit systems in terms of squared Rényi-\\(\\alpha \\) entanglement. Phys. Rev. A 93, 022306 (2016)\nLuo, Y., Tian, T., Shao, L.H., Li, Y.: General monogamy of Tsallis \\(q\\)-entropy entanglement in multiqubit systems. Phys. Rev. A 93, 062340 (2016)\nKumar, A., Dhar, H.S.: Lower bounds on the violation of the monogamy inequality for quantum correlation measures. Phys. Rev. A 93, 062337 (2016)\nJia, Z.A., Wu, Y.C., Guo, G.C.: Monogamy relation in no-disturbance theories. Phys. Rev. A 94, 012111 (2016)\nKim, J.S.: Tsallis entropy and general polygamy of multiparty quantum entanglement in arbitrary dimensions. Phys. Rev. A 94, 062338 (2016)\nCheng, S., Hall, M.J.W.: Anisotropic invariance and the distribution of quantum correlations. Phys. Rev. Lett. 118, 010401 (2017)\nAllen, G.W., Meyer, D.A.: Polynomial monogamy relations for entanglement negativity. Phys. Rev. Lett. 118, 080402 (2017)\nGour, G., Guo, Y.: Monogamy of Entanglement Without Inequalities. arXiv:1710.03295v1 [quant-ph]\nOllivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)\nHenderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. A 34, 6899 (2001)\nLuo, S., Fu, S.: Measurement-induced nonlocality. Phys. Rev. Lett. 106, 120401 (2011)\nOppenheim, J., Horodecki, M., Horodecki, P., Horodecki, R.: Thermodynamical approach to quantifying quantum correlations. Phys. Rev. Lett. 89, 180402 (2002)\nWiseman, H.M., Jones, S.J., Doherty, A.C.: Steering, entanglement, nonlocality, and the Einstein–Podolsky–Rosen paradox. Phys. Rev. Lett. 98, 140402 (2007)\nWu, S., Poulsen, U.V., Mølmer, K.: Correlations in local measurements on a quantum state, and complementarity as an explanation of nonclassicality. Phys. Rev. A 80, 032319 (2009)\nGroisman, B., Popescu, S., Winter, A.: Quantum, classical, and total amount of correlations in a quantum state. Phys. Rev. A 72, 032317 (2005)\nLuo, S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008)\nGuo, Y., Wu, S.: Quantum correlation exists in any non-product state. Sci. Rep. 4, 7179 (2014)\nGuo, Y., Li, X., Li, B., Fan, H.: Quantum correlation induced by the average distance between the reduced states. Int. J. Theor. Phys. 54(6), 2011–2030 (2015)\nKim, J.S.: Tsallis entropy and entanglement constraints in multiqubit systems. Phys. Rev. A 81, 062328 (2010)\nDiVincenzo, D.P., et al.: Entanglement of assistance. Lect. Notes Comput. Sci. 1509, 247 (1999)\nGuo, Y., Du, S., Li, X., Wu, S.: Entangled bases with fixed Schmidt number. J. Phys. A Math. Theor. 48, 245301 (2015)\nGuo, Y., Jia, Y., Li, X.: Multipartite unextendible entangled basis. Quantum Inf. Process. 14, 3553 (2015)",{"VOID":369},"10.1007\u002Fs11128-018-1996-5","2024-06-25T17:43:43.564+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs11128-018-1996-5",[373],{"id":374,"sortIndex":19,"researcher":18,"roles":375,"affiliations":376,"properties":393,"displayName":395,"givenName":18,"familyName":18},"628402fb-60fb-4678-a298-c7bf0aeb8861",[150],[377,385],{"id":378,"sortIndex":19,"affiliation":379,"properties":18},"bc02a7ff-9714-4825-ad47-044d27aacc79",{"id":378,"createTime":18,"updateTime":18,"relativeEntities":380,"slug":18,"properties":381,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":384,"statistic":18},[],{"title":382},{"VI":383},"Institute of Quantum Information Science, Shanxi Datong University, Datong, 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quantum key distribution (TF-QKD) can overcome the basic limits of QKD without repeaters. In practice, TF-QKD needs to optimize all parameters when limited data sets are considered. The traditional exhaustive traversal or local search algorithm can’t meet the time and resource requirements of the real-time communication system. Combined with machine learning, parameter optimization prediction of QKD has become the mainstream of parameter optimization. Random forest (RF) is a classical algorithm of the bagging class in integrated learning, and back-propagation neural network (BPNN) is an important algorithm in the neural network. This paper uses the extreme gradient boosting (XGBoost) of boosting class to predict the optimization parameters of TF-QKD and compares it with RF and BPNN. The results show that XGBoost can efficiently and accurately predict optimization parameters, and its performance is slightly better than RF and BPNN in parameter prediction, which can provide a reference for future real-time QKD networks.\n",{"EN":476},"Optimization parameter prediction-based XGBoost of TF-QKD",{"VOID":478},"[\"4699969539865944482\"]",{"VOID":480},"Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. Theor. Comput. Sci. 560, 7–11 (2014)\nEkert, A.K.: Quantum cryptography based on bell’s theorem. Phys. Rev. Lett. 67(6), 661 (1991)\nGisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Modern Phys. 74(1), 145 (2002)\nMayers, D.: Unconditional security in quantum cryptography. J. ACM 48(3), 351–406 (2001)\nTakeoka, M., Guha, S., Wilde, M.M.: Fundamental rate-loss tradeoff for optical quantum key distribution. Nat. Commun. 5(1), 1–7 (2014)\nPirandola, S., Laurenza, R., Ottaviani, C., Banchi, L.: Fundamental limits of repeaterless quantum communications. Nat. Commun. 8(1), 1–15 (2017)\nLo, H.-K., Curty, M., Qi, B.: Measurement-device-independent quantum key distribution. Phys. Rev. Lett. 108(13), 130503 (2012)\nYin, H.-L., Chen, T.-Y., Yu, Z.-W., Liu, H., You, L.-X., Zhou, Y.-H., Chen, S.-J., Mao, Y., Huang, M.-Q., Zhang, W.-J., et al.: Measurement-device-independent quantum key distribution over a 404 km optical fiber. Phys. Rev. Lett. 117(19), 190501 (2016)\nZhou, Y.-H., Yu, Z.-W., Wang, X.-B.: Making the decoy-state measurement-device-independent quantum key distribution practically useful. Phys. Rev. A 93(4), 042324 (2016)\nLucamarini, M., Yuan, Z.L., Dynes, J.F., Shields, A.J.: Overcoming the rate-distance limit of quantum key distribution without quantum repeaters. Nature 557(7705), 400–403 (2018)\nCurty, M., Azuma, K., Lo, H.-K.: Simple security proof of twin-field type quantum key distribution protocol. npj Quant. Inform. 5(1), 1–6 (2019)\nLin, J., Lütkenhaus, N.: Simple security analysis of phase-matching measurement-device-independent quantum key distribution. Phys. Rev. A 98(4), 042332 (2018)\nCui, C., Yin, Z.-Q., Wang, R., Chen, W., Wang, S., Guo, G.-C., Han, Z.-F.: Twin-field quantum key distribution without phase postselection. Phys. Rev. Appl. 11(3), 034053 (2019)\nJiang, C., Yu, Z.-W., Hu, X.-L., Wang, X.-B.: Sending-or-not-sending twin-field quantum key distribution with discrete-phase-randomized weak coherent states. Phys. Rev. Res. 2(4), 043304 (2020)\nHu, X.-L., Jiang, C., Yu, Z.-W., Wang, X.-B.: Sending-or-not-sending twin-field protocol for quantum key distribution with asymmetric source parameters. Phys. Rev. A 100(6), 062337 (2019)\nYu, Z.-W., Hu, X.-L., Jiang, C., Xu, H., Wang, X.-B.: Sending-or-not-sending twin-field quantum key distribution in practice. Sci. Rep. 9(1), 1–8 (2019)\nHe, S.-F., Wang, Y., Li, J.-J., Bao, W.-S.: Asymmetric twin-field quantum key distribution with both statistical and intensity fluctuations. Commun. Theor. Phys. 72(6), 065103 (2020)\nPark, J., Lee, J., Heo, J.: Improved statistical fluctuation analysis for twin-field quantum key distribution. Quantum Inf. Process. 20(4), 1–9 (2021)\nXu, F., Xu, H., Lo, H.-K.: Protocol choice and parameter optimization in decoy-state measurement-device-independent quantum key distribution. Phys. Rev. A 89(5), 052333 (2014)\nFerrari, D.: Client requirements for real-time communication services. IEEE Commun. Mag. 28(11), 65–72 (1990)\nRen, Z.-A., Chen, Y.-P., Liu, J.-Y., Ding, H.-J., Wang, Q.: Implementation of machine learning in quantum key distributions. IEEE Commun. Lett. 25(3), 940–944 (2020)\nWang, W., Lo, H.-K.: Machine learning for optimal parameter prediction in quantum key distribution. Phys. Rev. A 100(6), 062334 (2019)\nDing, H.-J., Liu, J.-Y., Zhang, C.-M., Wang, Q.: Predicting optimal parameters with random forest for quantum key distribution. Quantum Inf. Process. 19(2), 1–8 (2020)\nLu, F.-Y., Yin, Z.-Q., Wang, C., Cui, C.-H., Teng, J., Wang, S., Chen, W., Huang, W., Xu, B.-J., Guo, G.-C., et al.: Parameter optimization and real-time calibration of a measurement-device-independent quantum key distribution network based on a back propagation artificial neural network. JOSA B 36(3), 92–98 (2019)\nDong, Q., Huang, G., Cui, W., Jiao, R.-Z.: Parameter optimization in satellite-based measurement-device-independent quantum key distribution. Quantum Sci. Technol. 7, 015014 (2021)\nLiaw, A., Wiener, M., et al.: Classification and regression by randomforest. R News 2(3), 18–22 (2002)\nMeinshausen, N., Ridgeway, G.: Quantile regression forests. J. Mach. Learn. Res. 7(6), 983 (2006)\nKohonen, T.: An introduction to neural computing. Neural Netw. 1(1), 3–16 (1988)\nRumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning representations by back-propagating errors. Nature 323(6088), 533–536 (1986)\nChen, T., He, T., Benesty, M., Khotilovich, V., Tang, Y., Cho, H., et al.: Xgboost: extreme gradient boosting. R Package Version 1(4), 1–4 (2015)\nChen, T., Guestrin, C.: Xgboost: A scalable tree boosting system. In: Proceedings of the 22nd Acm Sigkdd international conference on knowledge discovery and data mining, pp. 785–794 (2016)\nMa, X., Zeng, P., Zhou, H.: Phase-matching quantum key distribution. Phys. Rev. X 8(3), 031043 (2018)\nWang, X.-B., Yu, Z.-W., Hu, X.-L.: Twin-field quantum key distribution with large misalignment error. Phys. Rev. A 98(6), 062323 (2018)\nWang, R., Yin, Z.-Q., Lu, F.-Y., Wang, S., Chen, W., Zhang, C.-M., Huang, W., Xu, B.-J., Guo, G.-C., Han, Z.-F.: Optimized protocol for twin-field quantum key distribution. Commun. Phys. 3(1), 1–7 (2020)\nMa, X., Qi, B., Zhao, Y., Lo, H.-K.: Practical decoy state for quantum key distribution. Phys. Rev. A 72(1), 012326 (2005)\nMa, X., Fung, C.-H.F., Razavi, M.: Statistical fluctuation analysis for measurement-device-independent quantum key distribution. Phys. Rev. A 86(5), 052305 (2012)\nSun, S.-H., Gao, M., Li, C.-Y., Liang, L.-M.: Practical decoy-state measurement-device-independent quantum key distribution. Phys. Rev. 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Lett. 105(16), 160401 (2010)",{"doi":1176},"10.1103\u002FPhysRevLett.105.160401",{"id":1178,"createTime":1179,"updateTime":1180,"relativeEntities":1181,"slug":1182,"properties":1183,"entityType":141,"verifyStatus":142,"verifyTime":1194,"verifyNote":144,"languages":18,"translateLanguages":18,"viewCount":19,"primaryUrl":1195,"fullTextUrl":18,"authors":1196,"publicationType":204,"publisherRelationship":1297,"citationCount":19,"citationInfo":1363,"publishDate":1366,"publishYear":1364,"citationAnalyzeStatus":1367,"lastCitationAnalyze":1368,"indexDatabases":1369,"openAccess":18,"references":18,"isForceReanalyzing":352},"953f1f60-0a8f-49e5-8118-0ad71835ee84","2024-01-14T22:37:41.523+00:00","2026-07-18T21:26:01.088+00:00",[],"Equivalence-of-classicality-and-separability-based-on-P-phase-space-representation-of-symmetric-multiqubit-states",{"abstract":1184,"title":1186,"gsPaper":1188,"references":1190,"doi":1192},{"EN":1185},"Classical and quantum world views differ in peculiar ways. Understanding decisive quantum features—for which no classical explanation exist—and their interrelations is of foundational interest. Moreover, recognizing non-classical features carries practical significance in information processing tasks as it offers insights as to why quantum protocols work better than their classical counterparts. We focus here on two celebrated notions of non-classicality viz., negativity of P phase–space representation and entanglement in symmetric multiqubit systems. We prove that they imply each other.",{"EN":1187},"Equivalence of classicality and separability based on P phase–space representation of symmetric multiqubit states",{"VOID":1189},"[\"5294910859647308160\",\"7325882017150360023\"]",{"VOID":1191},"Sudarshan, E.C.G.: Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams. Phys. Rev. Lett. 10, 277–279 (1963)\nGlauber, R.J.: Coherent and incoherent states of the radiation field. Phys. 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World Scientific, Singapore (1988)\nUsha Devi, A.R., Uma, M.S., Prabhu, R., Rajagopal, A.K.: Constraints on the uncertainties of entangled symmetric qubits. Phys. Lett. A 364, 203–207 (2007)\nUsha Devi, A.R., Uma, M.S., Prabhu, R., Sudha.: Local invariants and pairwise entanglement in symmetric multiqubit system. Int. J. Mod. Phys. B 20, 1917–1933 (2006)",{"VOID":1193},"10.1007\u002Fs11128-013-0627-4","2024-06-23T19:33:49.090+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs11128-013-0627-4",[1197,1222,1244,1267,1282],{"id":1198,"sortIndex":19,"researcher":18,"roles":1199,"affiliations":1200,"properties":1217,"displayName":1219,"givenName":18,"familyName":18},"a888f462-e049-4ebb-bd28-3260113e84ae",[150],[1201,1209],{"id":1202,"sortIndex":19,"affiliation":1203,"properties":18},"0f4e9790-160f-4d1a-b75f-60e15f57782d",{"id":1202,"createTime":18,"updateTime":18,"relativeEntities":1204,"slug":18,"properties":1205,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1208,"statistic":18},[],{"title":1206},{"VI":1207},"Department of Physics, Bangalore University, Bangalore, India",[],{"id":1210,"sortIndex":118,"affiliation":1211,"properties":18},"1775fa61-4497-4475-83eb-2c310811a072",{"id":1210,"createTime":18,"updateTime":18,"relativeEntities":1212,"slug":18,"properties":1213,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1216,"statistic":18},[],{"title":1214},{"VI":1215},"Inspire Institute Inc., Alexandria, USA",[],{"title":1218,"gsAuthor":1220},{"VI":1219},"A. 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With the present scheme, two \n$$W_{m+n+t-2}$$\n\n states can be created from an n-qubit W state, an m-qubit W state and a t-qubit W state, and two \n$$W_{m+n+t+q-3}$$\n\n states can be generated from \n$$W_m$$\n\n, \n$$W_n$$\n\n, \n$$W_t$$\n\n and \n$$W_q$$\n\n states. In the previous fusion schemes, only one particle from each initial W state is allowed to enter the fusion mechanism, but with the progress of experimental technology, two particles can be extracted. In this case, the W states fusion of our scheme will be realized without any ancillary particles and controlled quantum gate. In addition, compared with the one target W state obtained in previous preparation schemes, our scheme can generate two large-scale W states, which effectively improve the success rate of generating target W state. The ability to generate two target W states makes our scheme have a distinct advantage in preparing W states with larger particle numbers. This preparation mechanism also can be generalized to the case of fusing more different or same particles W states.",{"EN":1729},"W states fusion via polarization-dependent beam splitter",{"VOID":1731},"[\"4786295712051052569\"]",{"VOID":1733},"Raussendorf, R., Browne, D.E., Briegel, H.J.: Measurement-based quantum computation on cluster states. Phys. Rev. A 68, 022312 (2003)\nBennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)\nBouwmeester, D., Pan, J.W., Mattle, K., Eibl, M., Weinfurter, H., Zeilinger, A.: Experimental quantum teleportation. Nature 390, 575 (1997)\nÖzdemir, Ş.K., Bartkiewicz, K., Liu, Y.X., Miranowicz, A.: Teleportation of qubit states through dissipative channels: conditions for surpassing the no-cloning limit. Phys. Rev. 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J-affine variety codes have been successfully used to obtain quantum stabilizer codes with excellent parameters. In a previous paper we gave formulae for the dimension of this family of quantum codes, but no bound for the minimum distance was given. In this work, we show how to derive quantum stabilizer codes with designed minimum distance from J-affine variety codes and their subfield-subcodes. Moreover, this allows us to obtain new quantum codes, some of them either with better parameters, or with larger distances than the previously known codes.",{"EN":1888},"On the distance of stabilizer quantum codes from J-affine variety codes",{"VOID":1890},"[\"4819061136541797533\"]",{"VOID":1892},"Aly, S.A., Klappenecker, S., Sarvepalli, P.K.: On quantum and classical BCH codes. IEEE Trans. Inf. Theory 53, 1183–1188 (2007)\nAndersen, H.E., Geil, O.: Evaluation codes from order domain theory. Finite Fields Appl. 14, 92–123 (2008)\nAshikhmin, A., Barg, A., Knill, E., Litsyn, S.: Quantum error-detection I: statement of the problem. IEEE Trans. Inf. Theory 46, 778–788 (2000)\nAshikhmin, A., Barg, A., Knill, E., Litsyn, S.: Quantum error-detection II: bounds. IEEE Trans. Inf. Theory 46, 789–800 (2000)\nAshikhmin, A., Knill, E.: Non-binary quantum stabilizer codes. IEEE Trans. Inf. Theory 47, 3065–3072 (2001)\nBierbrauer, J., Edel, Y.: Quantum twisted codes. J. Comb. Des. 8, 174–188 (2000)\nCalderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.A.: Quantum error correction and orthogonal geometry. Phys. Rev. Lett. 76, 405–409 (1997)\nCalderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.A.: Quantum error correction via codes over GF(4). IEEE Trans. Inf. Theory 44, 1369–1387 (1998)\nCalderbank, A.R., Shor, P.: Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098–1105 (1996)\nChen, B., Ling, S., Zhang, G.: Application of constancyclic codes to quantum MDS codes. IEEE Trans. Inf. Theory 61, 1474–1484 (2015)\nCox, D., Little, J., O’Shea, D.: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. Undergraduate Texts in Mathematics, 4th edn. Springer-Verlag (2015).\nDieks, D.: Communication by EPR devices. Phys. Rev. A 92, 271 (1982)\nEdel, Y.: Some good quantum twisted codes. http:\u002F\u002Fwww.mathi.uni-heidelberg.de\u002F~yves\u002FMatritzen\u002FQTBCH\u002FQTBCHIndex.html\nEkert, A., Macchiavello, C.: Quantum error correction for communication. Phys. Rev. Lett. 77, 2585 (1996)\nFeng, K.: Quantum error correcting codes. In: Niederreiter, H. (ed) Coding Theory and Cryptology. pp. 91–142. Word Scientific. Singapore (2002)\nFeng, K., Ma, Z.: A finite Gilbert-Varshamov bound for pure stabilizer quantum codes. IEEE Trans. Inf. Theory 50, 3323–3325 (2004)\nGalindo, C., Hernando, F.: Quantum codes from affine variety codes and their subfield subcodes. Des. Codes Crytogr. 76, 89–100 (2015)\nGalindo, C., Hernando, F., Ruano, D.: New quantum codes from evaluation and matrix-product codes. Finite Fields Appl. 36, 98–120 (2015)\nGalindo, C., Hernando, F., Ruano, D.: Stabilizer quantum codes from \\(J\\)-affine variety codes and a new Steane-like enlargement. Quantum Inf. Process. 14, 3211–3231 (2015)\nGalindo, C., Pérez-Casales, R.: On the evaluation codes given by simple \\(\\delta \\)-sequences. AAECC 27, 59–90 (2016)\nGalindo, C., Monserrat, F.: Delta-sequences and evaluation codes defined by plane valuations at infinity. Proc. Lond. Math. Soc. 98, 714–740 (2009)\nGalindo, C., Monserrat, F.: Evaluation codes defined by finite families of plane valuations at infinity. Des. Codes Crytogr. 70, 189–213 (2014)\nGeil, O.: Evaluation codes from an affine variety code perspective. In: Martinez-Moro, E., Munuera, C., Ruano, D. (eds.) Advances in Algebraic Geometry Codes. Ser. Coding Theory Cryptol., vol. 5, pp. 153–180. World Scientific Publishing, Hackensack (2008)\nGeil, O.: Roots and coefficients of multivariate polynomials over finite fields. Finite Fields Appl. 23, 35–52 (2015)\nGeil, O., Høholdt, T.: On hyperbolic codes. Lect. Notes Comput. Sci. 2227, 159–171 (2001)\nGeil, O., Matsumoto, R., Ruano, D.: Feng–Rao decoding of primary codes. Finite Fields Appl. 34, 36–44 (2013)\nGeil, O., Thomsen, C.: Weighted Reed-Muller codes revisited. Des. Codes Cryptogr. 66, 195–220 (2013)\nGottesman, D.: A class of quantum error-correcting codes saturating the quantum Hamming bound. Phys. Rev. A 54, 1862–1868 (1996)\nGrassl, M.: Bounds on the minimum distance of linear codes. http:\u002F\u002Fwww.codetables.de (2015). Accessed 15 Feb 2015\nGrassl, M., Beth, T., Rötteler, M.: On optimal quantum codes. Int. J. Quantum Inform. 2, 757–775 (2004)\nGrassl, M., Rötteler, M.: Quantum BCH codes. In: Proc. X Int. Symp. Theor. elec. Eng. Germany (1999), pp. 207–212\nHamada, M.: Concatenated quantum codes constructible in polynomial time: efficient decoding and error correction. IEEE Trans. Inf. Theory 54, 5689–5704 (2008)\nHe, X., Xu, L., Chen, H.: New \\(q\\)-ary quantum MDS codes with distances bigger than \\(q\u002F2\\). Quantum Inf. Process. 15, 2745–2758 (2016)\nHøholdt, T.: On (or in) Dick Blahut’s footprint. In: Vardy, A (ed.) Codes, Curves and Signals. The Springer International Series in Engineering and Computer Science, vol. 485, pp. 3–7 (1998). http:\u002F\u002Flink.springer.com\u002Fchapter\u002F10.1007%2F978-1-4615-5121-8_1\nJin, L., Ling, S., Luo, J., Xing, C.: Application of classical Hermitian self-orthogonal MDS codes to quantum MDS codes. IEEE Trans. Inf. Theory 56, 4735–4740 (2010)\nKetkar, A., Klappenecker, A., Kumar, S., Sarvepalli, P.K.: Nonbinary stabilizer codes over finite fields. IEEE Trans. Inf. Theory 52, 4892–4914 (2006)\nLa Guardia, G.G.: Construction of new families of nonbinary quantum BCH codes. Phys. Rev. A 80, 042331 (2009)\nLa Guardia, G.G.: On the construction of nonbinary quantum BCH codes. IEEE Trans. Inf. Theory 60, 1528–1535 (2014)\nLa Guardia, G.G., Palazzo, R.: Constructions of new families of nonbinary CSS codes. Discrete Math. 310, 2935–2945 (2010)\nMassey, J.L., Costello, D.J., Justensen, J.: Polynomial weights and code constructions. IEEE Trans. Inf. Theory 19, 101–110 (1973)\nMatsumoto, R., Uyematsu, T.: Constructing quantum error correcting codes for \\(p^m\\) state systems from classical error correcting codes. IEICE Trans. Fundam. E83–A, 1878–1883 (2000)\nMatsumoto, R., Uyematsu, T.: Lower bound for the quantum capacity of a discrete memoryless quantum channel. J. Math. Phys 43, 4391–4403 (2002)\nSaints, K., Heegard, C.: On hyperbolic cascaded Reed-Solomon codes. Lect. Notes Comput. Sci. 673, 291–303 (1993)\nSarvepalli, P.K., Klappenecker, A.: Nonbinary quantum Reed-Muller codes. In: Proc. 2005 Int. Symp. Information Theory, pp. 1023–1027\nShor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. In: Proc. 35th ann. symp. found. comp. sc., IEEE Comp. Soc. Press (1994), pp. 124–134\nShor, P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, 2493–2496 (1995)\nSteane, A.M.: Simple quantum error correcting codes. Phys. Rev. Lett. 77, 793–797 (1996)\nSteane, A.M.: Enlargement of calderbank-shor-steane quantum codes. IEEE Trans. Inf. Theory 45, 2492–2495 (1999)\nWootters, W.K., Zurek, W.H.: A single quantum cannot be cloned. Nature 299, 802–803 (1982)\nYu, S., Bierbrauer, J., Dong, Y., Chen, Q., Oh, C.H.: All the stabilizer codes of distance 3. IEEE Trans. Inf. Theory 59, 5179–5185 (2013)",{"VOID":1894},"10.1007\u002Fs11128-017-1559-1","2024-06-23T15:45:36.794+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs11128-017-1559-1",[1898,1915,1930,1945],{"id":1899,"sortIndex":19,"researcher":18,"roles":1900,"affiliations":1901,"properties":1910,"displayName":1912,"givenName":18,"familyName":18},"2c74afe5-f5b4-461a-9511-34b46f91b4eb",[150],[1902],{"id":1903,"sortIndex":19,"affiliation":1904,"properties":18},"be7506ec-1419-4ca0-b799-2b9d26e2d38f",{"id":1903,"createTime":18,"updateTime":18,"relativeEntities":1905,"slug":18,"properties":1906,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1909,"statistic":18},[],{"title":1907},{"EN":1908},"Instituto Universitario de Matemáticas y Aplicaciones de Castellón and Departamento de Matemáticas, Universitat Jaume I, Castelló, Spain",[],{"title":1911,"gsAuthor":1913},{"VI":1912},"Carlos 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detection, as a fundamental problem in image processing and computer vision, is an indispensable task in digital image processing. Because of the sharp increase in the image data in the actual applications, real-time problem has become a limitation in classical image processing. In this paper, based on the novel enhanced quantum image representation (NEQR) of digital images, an enhanced quantum edge detection algorithm is investigated, which combines the classical Laplacian operator and zero-cross method. Because NEQR utilizes the superposition state of qubit sequence to store all the pixels of an image, the corresponding quantum image edge detection algorithm can realize parallel computation to implement the Laplacian filter and further calculate the image intensity of all the pixels according zero-cross method. The circuit complexity analysis demonstrates that our presented quantum image edge algorithm can reach a significant and exponential speedup compared to classical counterparts. Hence, our proposed quantum image edge detection algorithm would resolve the real-time problem of image edge extraction in practice image processing.",{"EN":2044},"Quantum image edge extraction based on Laplacian operator and zero-cross method",{"VOID":365},{"VOID":2047},"Yan, F., Iliyasu, A.M., Le, P.Q.: Quantum image processing: A review of advances in its security technologies. Int. J. Quant. Inf. 15(03), 1730001 (2017)\nYan, F., Iliyasu, A.M., Venegas-Andraca, S.E.: A Survey of Quantum Image Representations, vol. 15, pp. 1–35. Kluwer Academic Publishers, Hingham (2016)\nIliyasu, A.M.: Towards the realisation of secure and efficient image and video processing applications on quantum computers. Entropy 15, 2874–2974 (2013)\nIliyasu, A.M.: Algorithmic frameworks to support the realisation of secure and efficient image-video processing applications on quantum computers. Ph.D. (Dr Eng.) Thesis, Tokyo Institute of Technology, Tokyo, Japan. 25 Sept. 2012\nIliyasu, A.M., Le, P.Q., Yan, F., Bo, S., Garcia, J.A.S., Dong, F., Hirota, K.: A two-tier scheme for greyscale quantum image watermarking and recovery. Int. J. Innov. Comput. Appl. 5, 85–101 (2013)\nFeynman, R.: Simulating Physics with Computers, vol. 21, pp. 467–488. Perseus Books, Cambridge (1999)\nDeutsch, D.: Quantum theory, the church-turing principle and the universal quantum computer. Proc. R. Soc. Lond. 400, 97–117 (1985)\nShor, P.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pp. 124–134 (1994)\nGrover, L.: A fast quantum mechanical algorithm for database search. In: Proceedings of the 28th Annual ACM Symposium on Theory of Computing, pp. 212–219 (1996)\nVlasov, A.Y.: Quantum computations and images recognition (1997). arXiv:quant-ph\u002F9703010\nLugiato, L.A., Gatti, A., Brambilla, E.: Quantum imaging. J. Opt. B 4, 176–184 (2002)\nEldar, Y.C., Oppenheim, A.V.: Quantum signal processing. IEEE Signal Process. Mag. 19, 12–32 (2001)\nSchützhold, R.: Pattern recognition on a quantum computer. Phys. Rev. A 67(6), 062311 (2003)\nVenegas-Andraca,S., Bose, S.: Storing, processing, and retrieving an image using quantum mechanics. In: Proceedings of SPIE Conference of Quantum Information and Computation, vol. 5105, pp. 134–147 (2003)\nVenegas-Andraca, S., Ball, J.: Processing images in entangled quantum systems. Quant. Inf. Process. 9, 1–11 (2010)\nLatorre, J.: Image compression and entanglement (2005). arXiv:quant-ph\u002F0510031\nLe, P., Dong, F., Hirota, K.: A flexible representation of quantum images for polynomial preparation, image compression, and processing operations. Quant. Inf. Process. 10, 63–84 (2011)\nZhang, Y., Lu, K., Gao, Y., Mao, W.: NEQR: a novel enhanced quantum representation of digital images. Quant. Inf. Process. 12, 2833–2860 (2013)\nZhang, Y., Lu, K., Gao, Y., Xu, K.: A novel quantum representation for log-polar images. Quant. Inf. Process. 12, 3103–3126 (2013)\nLi, H., Zhu, Q., Lan, S., Shen, C., Zhou, R., et al.: Image storage, retrieval, compression and segmentation in a quantum system. Quant. Inf. Process. 12, 2269–2290 (2013)\nLi, H., Zhu, Q., Zhou, R., Song, L., Yang, X.: Multi-dimensional color image storage and retrieval for a normal arbitrary quantum superposition state. Quant. Inf. Process. 13, 991–1011 (2014)\nYuan, S., Mao, X., Xue, Y., Chen, L., Xiong, Q., et al.: SQR: a simple quantum representation of infrared images. Quant. Inf. Process. 13, 1353–1379 (2014)\nSang, J., Wang, S., Li, Q.: A novel quantum representation of color digital images. Quant. Inf. Process. 16, 42 (2017)\nLe, P.Q., Iliyasu, A.M., Dong, F., et al.: Fast geometric transformations on quantum images. Iaeng Int. J. Appl. Math. 40(3), 113–123 (2010)\nLe, P.Q., Iliyasu, A.M., Dong, F., et al.: Strategies for designing geometric transformations on quantum images. Theoret. Comput. Sci. 412, 1406–1418 (2011)\nFan, P., Zhou, R., Jing, N., Li, H.: Geometric transformations of multidimensional color images based on NASS. Inf. Sci. 340, 191–208 (2016)\nWang, J., Jiang, N., Wang, L.: Quantum image translation. Quant. Inf. Process. 14, 1589–1604 (2015)\nZhou, R.-G., Tan, C., Ian, H.: Global and local translation designs of quantum image based on FRQI. Int. J. Theor. 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employing Pauli measurements, we present some nonlinear steering criteria applicable for arbitrary two-qubit quantum systems and optimized ones for symmetric quantum states. These criteria provide sufficient conditions to witness steering, which can recover the previous elegant results for some well-known states. Compared with the existing linear steering criterion and entropic criterion, ours can certify more steerable states without selecting measurement settings or correlation weights, which can also be used to verify entanglement as all steerable quantum states are entangled.",{"EN":2191},"Nonlinear steering criteria for arbitrary two-qubit quantum systems",{"VOID":365},{"VOID":2194},"Einstein, A., Podolsky, B., Rosen, N.: Can it quantum mechanical description of physical reality be considered complete? Phys. Rev. 47(10), 777 (1935)\nSchrödinger, E.: Probability relations between separated systems. Proc. Cambridge Philos. Soc. 32(3), 446 (1936)\nWiseman, H.M., Jones, S.J., Doherty, A.C.: Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox. Phys. Rev. Lett. 98(14), 140402 (2007)\nReid, M.D.: Signifying quantum benchmarks for qubit teleportation and secure quantum communication using Einstein-Podolsky-Rosen steering inequalities. Phys. Rev. A 88(6), 062338 (2013)\nHe, Q., Rosales-Zárate, L., Adesso, G., Reid, M.D.: Secure Continuous Variable Teleportation and Einstein-Podolsky-Rosen Steering. Phys. Rev. Lett. 115(18), 180502 (2015)\nWalk, N., Hosseini, S., Geng, J., Thearle, O., Haw, J.Y., Armstrong, S., Assad, S.M., Janousek, J., Ralph, T.C., Symul, T., Wiseman, H.M., Lam, P.K.: Experimental demonstration of Gaussian protocols for one-sided device-independent quantum key distribution. Optica 3(6), 634 (2016)\nKogias, I., Xiang, Y., He, Q., Adesso, G.: Unconditional security of entanglement-based continuous-variable quantum secret sharing. Phys. Rev. A 95(1), 012315 (2017)\nBranciard, C., Cavalcanti, E.G., Walborn, S.P., Scarani, V., Wiseman, H.M.: One-sided device-independent quantum key distribution: Security, feasibility, and the connection with steering. Phys. Rev. A 85(1), 010301(R) (2012)\nPiani, M., Watrous, J.: Necessary and Sufficient Quantum Information Characterization of Einstein-Podolsky-Rosen Steering. Phys. Rev. Lett. 114(6), 060404 (2015)\nHorodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81(2), 865 (2009)\nBell, J.S.: On the Einstein-Podolsky-Rosen Porodox. Physics 1, 195 (1964)\nJones, S.J., Wiseman, H.M., Doherty, A.C.: Entanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering. Phys. Rev. A 76(5), 052116 (2007)\nBrunner, N., Cavalcanti, D., Pironio, S., Scarant, V., Wehner, S.: Bell nonlocality. Rev. Mod. Phys. 86(2), 419 (2014)\nBowles, J., Vértesi, T., Quintino, M.T., Brunner, N.: One-way Einstein-Podolsky-Rosen Steering. Phys. Rev. Lett. 112(20), 200402 (2014)\nHändchen, V., Eberle, T., Steinlechner, S., Samblowski, A., Franz, T., Werner, R.F., Schnabel, R.: Observation of one-way Einstein-Podolsky-Rosen steering. Nature Photonics 6, 596 (2012)\nWollmann, S., Walk, N., Bennet, A.J., Wiseman, H.M., Pryde, G.J.: Observation of Genuine One-Way Einstein-Podolsky-Rosen Steering. Phys. Rev. Lett. 116(16), 160403 (2016)\nSaunders, D.J., Jones, S.J., Wiseman, H.M., Pryde, G.J.: Experimental EPR-steering using Bell-local states. Nat. Phys. 6, 845 (2010)\nSchneeloch, J., Broadbent, C.J., Walborn, S.P., Cavalcanti, E.G., Howell, J.C.: Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations. Phys. Rev. A 87(6), 062103 (2013)\nJi, S.W., Lee, J., Park, J., Nha, H.: Steering criteria via covariance matrices of local observables in arbitrary-dimensional quantum systems. Phys. Rev. A 92(6), 062130 (2015)\nZhen, Y.Z., Zheng, Y.L., Cao, W.F., Li, L., Chen, Z.B., Liu, N.L., Chen, K.: Certifying Einstein-Podolsky-Rosen steering via the local uncertainty principle. Phys. Rev. A 93(1), 012108 (2016)\nZheng, Y.L., Zhen, Y.Z., Chen, Z.B., Liu, N.L., Chen, K., Pan, J.W.: Efficient linear criterion for witnessing Einstein-Podolsky-Rosen nonlocality under many-setting local measurements. Phys. Rev. A 95(1), 012142 (2017)\nZheng, Y.L., Zhen, Y.Z., Cao, W.F., Li, L., Chen, Z.B., Liu, N.L., Chen, K.: Optimized detection of steering via linear criteria for arbitrary-dimensional states. Phys. Rev. A 95(3), 032128 (2017)\nYu, S.X., Chen, Q., Zhang, C.J., Lai, C.H., Oh, C.H.: All Entangled Pure States Violate a Single Bell’s Inequality. Phys. Rev. Lett. 109(12), 120402 (2012)\nPearson, K.: The London, Edinburgh, and Dublin Philosophical Magazine and Journal of. Science 2, 559–572 (1901)\nHotelling, H.: Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology 24(6), 417 (1933)\nJolliffe, I.T.: Principal Component Analysis. Series: Springer Series in Statistics, 2nd ed., Springer (2002)\nGross, D.J.: Symmetry in Physics: Wigner’s Legacy. Phys. Today 48(12), 46 (1995)\nVollbrecht, K.G.H., Werner, R.F.: Entanglement measures under symmetry. Phys. Rev. A 64(6), 062307 (2001)\nStockton, J.K., Geremia, J.M., Doherty, A.C., Mabuchi, H.: Characterizing the entanglement of symmetric many-particle spin-1\u002F2 systems. Phys. Rev. A 67(2), 022112 (2003)\nTáth, G., Gühne, O.: Entanglement and Permutational Symmetry. Phys. Rev. Lett. 102(7), 170503 (2009)\nWerner, R.F.: Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40(8), 4277 (1989)\nGisin, N.: Hidden quantum nonlocality revealed by local filters. Phys. Lett. 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