{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T03:55:22Z","timestamp":1775534122027,"version":"3.50.1"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2009,12,18]],"date-time":"2009-12-18T00:00:00Z","timestamp":1261094400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2010,12]]},"DOI":"10.1007\/s11128-009-0159-0","type":"journal-article","created":{"date-parts":[[2009,12,17]],"date-time":"2009-12-17T05:44:54Z","timestamp":1261028694000},"page":"699-710","source":"Crossref","is-referenced-by-count":16,"title":["Temperley\u2013Lieb algebra, Yang-Baxterization and universal gate"],"prefix":"10.1007","volume":"9","author":[{"given":"Gangcheng","family":"Wang","sequence":"first","affiliation":[]},{"given":"Kang","family":"Xue","sequence":"additional","affiliation":[]},{"given":"Chunfang","family":"Sun","sequence":"additional","affiliation":[]},{"given":"Chengcheng","family":"Zhou","sequence":"additional","affiliation":[]},{"given":"Taotao","family":"Hu","sequence":"additional","affiliation":[]},{"given":"Qingyong","family":"Wang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2009,12,18]]},"reference":[{"key":"159_CR1","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1038\/35005001","volume":"404","author":"C.H. Bennett","year":"2000","unstructured":"Bennett C.H., DiVincenzo D.P.: Quantum information and computation. Nature 404, 247 (2000)","journal-title":"Nature"},{"key":"159_CR2","doi-asserted-by":"crossref","first-page":"1895","DOI":"10.1103\/PhysRevLett.70.1895","volume":"70","author":"C.H. Bennett","year":"1993","unstructured":"Bennett C.H., Brassard G., Cr\u00e9peau C., Jozsa R., Peres W.K., Wootters A.: Teleporting an unknown quantum state via dual classical and Einstein\u2013Podolsky\u2013Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)","journal-title":"Phys. Rev. Lett."},{"key":"159_CR3","doi-asserted-by":"crossref","first-page":"2881","DOI":"10.1103\/PhysRevLett.69.2881","volume":"69","author":"C.H. Bennett","year":"1992","unstructured":"Bennett C.H., Wiesner S.J.: Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 2881 (1992)","journal-title":"Phys. Rev. Lett."},{"key":"159_CR4","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1103\/PhysRevA.59.156","volume":"59","author":"M. Murao","year":"1999","unstructured":"Murao M., Jonathan D., Plenio M.B., Vedral V.: Quantum telecloning and multiparticle entanglement. Phys. Rev. A 59, 156 (1999)","journal-title":"Phys. Rev. A"},{"key":"159_CR5","doi-asserted-by":"crossref","unstructured":"Kauffman, L.H.: Knots and Physics. World Scientific Publishers (2002)","DOI":"10.1142\/9789812384836"},{"key":"159_CR6","doi-asserted-by":"crossref","unstructured":"Kauffman, L.H., Lomonaco Jr., S.J.: Braiding operators are universal quantum gates. New J. Phys. 4, 73.1C73.18 (2002)","DOI":"10.1088\/1367-2630\/4\/1\/373"},{"key":"159_CR7","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Kauffman, L.H., Ge, M.-L.: Yang CBaxterizations, Universal quantum gates and Hamiltonians. Quant. Inf. Process. 4(3), August (2005)","DOI":"10.1007\/s11128-005-7655-7"},{"key":"159_CR8","doi-asserted-by":"crossref","first-page":"1312","DOI":"10.1103\/PhysRevLett.19.1312","volume":"19","author":"C.N. Yang","year":"1967","unstructured":"Yang C.N.: Some Exact results for the many-body problem in one dimension with repulsive delta-function interaction. Phys. Rev. Lett. 19, 1312 (1967)","journal-title":"Phys. Rev. Lett."},{"key":"159_CR9","doi-asserted-by":"crossref","first-page":"1920","DOI":"10.1103\/PhysRev.168.1920","volume":"168","author":"C.N. Yang","year":"1968","unstructured":"Yang C.N.: S matrix for the one-dimensional N-body problem with repulsive or attractive-function interaction. Phys. Rev. 168, 1920 (1968)","journal-title":"Phys. Rev."},{"key":"159_CR10","volume-title":"Exactly Solved Models in Statistical Mechanics","author":"R.J. Baxter","year":"1982","unstructured":"Baxter R.J.: Exactly Solved Models in Statistical Mechanics. Academic Press, London (1982)"},{"key":"159_CR11","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/0003-4916(72)90335-1","volume":"70","author":"R.J. Baxter","year":"1972","unstructured":"Baxter R.J.: Partition funtion of the eighy-vertex lattice model. Ann. Phys. 70, 193 (1972)","journal-title":"Ann. Phys."},{"key":"159_CR12","first-page":"254","volume":"32","author":"V.G. Drinfeld","year":"1985","unstructured":"Drinfeld V.G.: Hopf algebras and the quantum Yang\u2013Baxter equation. Soviet Math. Dokl 32, 254\u2013258 (1985)","journal-title":"Soviet Math. Dokl"},{"key":"159_CR13","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1142\/S0219749905001547","volume":"3","author":"Y. Zhang","year":"2005","unstructured":"Zhang Y., Kauffman L.H., Ge M.L.: Universal quantum gate, Yang Baxterization and Hamiltonian. Int. J. Quant. Inf. 3, 669 (2005)","journal-title":"Int. J. Quant. Inf."},{"key":"159_CR14","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/s11128-007-0064-3","volume":"6","author":"Y. Zhang","year":"2007","unstructured":"Zhang Y., Ge M.L.: GHZ states, almost-complex structure and Yang\u2013Baxter equation. Quant. Inf. Proc. 6, 363 (2007)","journal-title":"Quant. Inf. Proc."},{"key":"159_CR15","unstructured":"Zhang, Y., Rowell, E.C., Wu, Y.S., Wang, Z.H., Ge M.L.: From extraspecial two-Groups to GHZ states, e-print quant-ph\/0706.1761 (2007)."},{"key":"159_CR16","doi-asserted-by":"crossref","first-page":"042324","DOI":"10.1103\/PhysRevA.76.042324","volume":"76","author":"J.L. Chen","year":"2007","unstructured":"Chen J.L., Xue K., Ge M.L.: Braiding transformation, entanglement swapping, and Berry phase in entanglement space. Phys. Rev. A 76, 042324 (2007)","journal-title":"Phys. Rev. A"},{"key":"159_CR17","doi-asserted-by":"crossref","first-page":"2614","DOI":"10.1016\/j.aop.2008.06.003","volume":"323","author":"J.L. Chen","year":"2008","unstructured":"Chen J.L., Xue K., Ge M.L.: Berry phase and quantum criticality in Yang Baxter systems. Ann. Phys. 323, 2614 (2008)","journal-title":"Ann. Phys."},{"key":"159_CR18","doi-asserted-by":"crossref","first-page":"080306","DOI":"10.1088\/0256-307X\/26\/8\/080306","volume":"26","author":"J.L. Chen","year":"2009","unstructured":"Chen J.L., Xue K., Ge M.L.: All pure two-qudit entangled states can be generated via a universal Yang CBaxter matrix assisted by local unitary transformations. Chin. Phys. Lett. 26, 080306 (2009)","journal-title":"Chin. Phys. Lett."},{"key":"159_CR19","doi-asserted-by":"crossref","first-page":"022319","DOI":"10.1103\/PhysRevA.78.022319","volume":"78","author":"S.-W. Hu","year":"2008","unstructured":"Hu S.-W., Xue K., Ge M.-L.: Optical simulation of the Yang\u2013Baxter equation. Phys. Rev. A 78, 022319 (2008)","journal-title":"Phys. Rev. A"},{"key":"159_CR20","doi-asserted-by":"crossref","first-page":"052324","DOI":"10.1103\/PhysRevA.78.052324","volume":"78","author":"M.-G. Hu","year":"2008","unstructured":"Hu M.-G., Xue K., Ge M.-L.: Exact solution of a Yang\u2013Baxter spin-1\/2 chain model and quantum entanglement. Phys. Rev. A 78, 052324 (2008)","journal-title":"Phys. Rev. A"},{"key":"159_CR21","doi-asserted-by":"crossref","first-page":"125207","DOI":"10.1088\/1751-8113\/42\/12\/125207","volume":"42","author":"G. Wang","year":"2009","unstructured":"Wang G., Xue K., Wu C., Liang H., Oh C.H.: Entanglement and the Berry Phase in a new Yang\u2013Baxter System. J. Phys. A Math. Theor. 42, 125207 (2009)","journal-title":"J. Phys. A Math. Theor."},{"key":"159_CR22","doi-asserted-by":"crossref","unstructured":"Wang, G., Sun C., Wang Q., Xue K.: Entanglement and Berry Phase in a (3\u00a0\u00d7\u00a03)-dimensional Yang\u2013Baxter System, Int. J. Theor. Phys. doi: 10.1007\/s10773-009-0077-z","DOI":"10.1007\/s10773-009-0077-z"},{"key":"159_CR23","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1098\/rspa.1971.0067","volume":"322","author":"H. Temperley","year":"1971","unstructured":"Temperley H., Lieb E.H.: Relations between the percolation and colouring problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the percolation problem. Proc. R. Soc. (Lond) A 322, 251 (1971)","journal-title":"Proc. R. Soc. (Lond) A"},{"key":"159_CR24","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/0370-1573(89)90123-3","volume":"180","author":"M. Wadati","year":"1989","unstructured":"Wadati M., Deguchi T., Akutsu Y.: Exactly solvable models and knot theory. Phys. Rep. 180, 247 (1989)","journal-title":"Phys. Rep."},{"key":"159_CR25","doi-asserted-by":"crossref","first-page":"11599","DOI":"10.1088\/0305-4470\/39\/37\/017","volume":"39","author":"Y. Zhang","year":"2006","unstructured":"Zhang Y.: Teleportation, braid group and Temperley\u2013Lieb algebra. J. Phys. A Math. Gen. 39, 11599\u201311622 (2006)","journal-title":"J. Phys. A Math. Gen."},{"key":"159_CR26","doi-asserted-by":"crossref","first-page":"3313","DOI":"10.1103\/PhysRevLett.85.3313","volume":"85","author":"H. Bechmann-Pasquinucci","year":"2000","unstructured":"Bechmann-Pasquinucci H., Peres A.: Quantum cryptography with 3-state systems. Phys. Rev. Lett. 85, 3313 (2000)","journal-title":"Phys. Rev. Lett."},{"key":"159_CR27","doi-asserted-by":"crossref","first-page":"012310","DOI":"10.1103\/PhysRevA.67.012310","volume":"67","author":"D. Kaszlikowski","year":"2003","unstructured":"Kaszlikowski D. et\u00a0al.: Quantum cryptography based on qutrit Bell inequalities. Phys. Rev. A 67, 012310 (2003)","journal-title":"Phys. Rev. A"},{"key":"159_CR28","doi-asserted-by":"crossref","first-page":"127901","DOI":"10.1103\/PhysRevLett.88.127901","volume":"88","author":"D. Bruss","year":"2002","unstructured":"Bruss D., Machiavello C.: Optimal eavesdropping in cryptography with three-dimensional quantum states. Phys. Rev. Lett. 88, 127901 (2002)","journal-title":"Phys. Rev. Lett."},{"key":"159_CR29","doi-asserted-by":"crossref","first-page":"012311","DOI":"10.1103\/PhysRevA.67.012311","volume":"67","author":"Y.-C. Ou","year":"2003","unstructured":"Ou Y.-C. et\u00a0al.: Proper monogamy inequality for arbitrary pure quantum states. Phys. Rev. A 67, 012311 (2003)","journal-title":"Phys. Rev. A"},{"key":"159_CR30","doi-asserted-by":"crossref","first-page":"230503","DOI":"10.1103\/PhysRevLett.93.230503","volume":"93","author":"Y.I. Bogdanov","year":"2004","unstructured":"Bogdanov Y.I. et\u00a0al.: Quantum state engineering with qutrits. Phys. Rev. Lett. 93, 230503 (2004)","journal-title":"Phys. Rev. Lett."},{"key":"159_CR31","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1088\/1367-2630\/7\/1\/174","volume":"7","author":"D.M. Hugh","year":"2005","unstructured":"Hugh D.M., Twamley J.: Trapped-ion qutrit spin molecule quantum computer. New J. Phys. 7, 174 (2005)","journal-title":"New J. Phys."},{"key":"159_CR32","unstructured":"Beliczynski, B., et\u00a0al. (eds.): ICANNGA 2007, Part I, LNCS 4431, 120\u2013127"},{"key":"159_CR33","doi-asserted-by":"crossref","first-page":"3735","DOI":"10.1142\/S0217751X91001817","volume":"6","author":"M.L. Ge","year":"1991","unstructured":"Ge M.L., Xue K., Wu Y-S.: Explicit trigonometric Yang-Baxterization. Int. J. Mod. Phys. A 6, 3735 (1991)","journal-title":"Int. J. Mod. Phys. A"},{"key":"159_CR34","doi-asserted-by":"crossref","first-page":"023510","DOI":"10.1063\/1.2873025","volume":"49","author":"P.P. Kulish","year":"2008","unstructured":"Kulish P.P., Manojlovic N., Nagy Z.: Quantum symmetry algebras of spin systems related to Temperley\u2013Lieb R-matrices. J. Math. Phys. 49, 023510 (2008)","journal-title":"J. Math. Phys."},{"key":"159_CR35","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1103\/RevModPhys.80.1083","volume":"80","author":"C. Nayak","year":"2008","unstructured":"Nayak C., Simon S.H., Stern A., Freedman M., Sarma S.D.: Non-abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083 (2008)","journal-title":"Rev. Mod. Phys."},{"key":"159_CR36","unstructured":"Juan Ospina made a Mathematica implementation of our method, and the results in this paper were re-obtained"},{"key":"159_CR37","doi-asserted-by":"crossref","DOI":"10.1201\/9781420035377","volume-title":"Mathematics of Quantum Computation","author":"J.L. Brylinski","year":"2002","unstructured":"Brylinski J.L., Brylinski R.: Universal quantum gates. In: Brylinski, R., Chen, G. (eds) Mathematics of Quantum Computation, Chapman and Hall\/CRC Press, Boca Raton (2002)"},{"key":"159_CR38","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1103\/PhysRevA.58.883","volume":"58","author":"K. Zyczkowski","year":"1998","unstructured":"Zyczkowski K. et\u00a0al.: Volume of the set of separable states. Phys. Rev. A 58, 883 (1998)","journal-title":"Phys. Rev. A"},{"key":"159_CR39","doi-asserted-by":"crossref","first-page":"10759","DOI":"10.1088\/1751-8113\/40\/35\/003","volume":"40","author":"X. Wang","year":"2007","unstructured":"Wang X. et\u00a0al.: Negativity, entanglement witnesses and quantum phase transition in spin-1 Heisenberg chains. J. Phys. A Math. Theor. 40, 10759\u201310767 (2007)","journal-title":"J. Phys. A Math. Theor."},{"key":"159_CR40","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/j.physleta.2006.05.050","volume":"358","author":"R. Eryigit","year":"2006","unstructured":"Eryigit R., Guc Y., Eryigit R.: Analytical study of thermal entanglment in a two-dimensional J 1\u2212J 2 model. Phys. Lett. A 358, 363 (2006)","journal-title":"Phys. Lett. A"},{"key":"159_CR41","first-page":"484C488","volume":"281","author":"X.S. Ma","year":"2008","unstructured":"Ma X.S.: Thermal entanglement of a two-qutrit XX spin chain with Dzialoshinski Moriya interaction. Opt. Commun. 281, 484C488 (2008)","journal-title":"Opt. Commun."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-009-0159-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11128-009-0159-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-009-0159-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T07:36:28Z","timestamp":1559374588000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11128-009-0159-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,12,18]]},"references-count":41,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2010,12]]}},"alternative-id":["159"],"URL":"https:\/\/doi.org\/10.1007\/s11128-009-0159-0","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"value":"1570-0755","type":"print"},{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,12,18]]}}}