{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T02:18:27Z","timestamp":1770776307727,"version":"3.50.0"},"reference-count":13,"publisher":"Springer Science and Business Media LLC","issue":"2-3","license":[{"start":{"date-parts":[[2008,6,1]],"date-time":"2008-06-01T00:00:00Z","timestamp":1212278400000},"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":[[2008,6]]},"DOI":"10.1007\/s11128-008-0077-6","type":"journal-article","created":{"date-parts":[[2008,6,24]],"date-time":"2008-06-24T14:44:52Z","timestamp":1214318692000},"page":"117-124","source":"Crossref","is-referenced-by-count":3,"title":["Relation of operator Schmidt decomposition and CNOT complexity"],"prefix":"10.1007","volume":"7","author":[{"given":"Mark W.","family":"Coffey","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ron","family":"Deiotte","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2008,6,25]]},"reference":[{"key":"77_CR1","doi-asserted-by":"crossref","first-page":"012310","DOI":"10.1103\/PhysRevA.70.012310","volume":"70","author":"V.V. Shende","year":"2004","unstructured":"Shende V.V., Bullock S.S., Markov I.L.: Recognizing small-circuit structure in two-qubit operators. Phys. Rev. A 70, 012310 (2004)","journal-title":"Phys. Rev. A"},{"key":"77_CR2","doi-asserted-by":"crossref","first-page":"012318","DOI":"10.1103\/PhysRevA.68.012318","volume":"68","author":"S.S. Bullock","year":"2003","unstructured":"Bullock S.S., Markov I.L.: Arbitrary two-qubit computation in 23 elementary gates. Phys. Rev. A 68, 012318 (2003)","journal-title":"Phys. Rev. A"},{"key":"77_CR3","doi-asserted-by":"crossref","first-page":"010301(R)","DOI":"10.1103\/PhysRevA.69.010301","volume":"69","author":"G. Vidal","year":"2004","unstructured":"Vidal G., Dawson C.M.: Universal quantum circuit for two-qubit transformations with three controlled-not gates. Phys. Rev. A 69, 010301(R) (2004)","journal-title":"Phys. Rev. A"},{"key":"77_CR4","doi-asserted-by":"crossref","first-page":"032315","DOI":"10.1103\/PhysRevA.69.032315","volume":"69","author":"F. Vatan","year":"2004","unstructured":"Vatan F., Williams C.: Optimal quantum circuits for general two-qubit gates. Phys. Rev. A 69, 032315 (2004)","journal-title":"Phys. Rev. A"},{"key":"77_CR5","doi-asserted-by":"crossref","first-page":"042313","DOI":"10.1103\/PhysRevA.67.042313","volume":"67","author":"J. Zhang","year":"2003","unstructured":"Zhang J., Vala J., Whaley K.B., Sastry S.: A geometric theory of non-local two-qubit operations. Phys. Rev. A 67, 042313 (2003)","journal-title":"Phys. Rev. A"},{"key":"77_CR6","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1023\/A:1022144002391","volume":"1","author":"Y. Makhlin","year":"2002","unstructured":"Makhlin Y.: Nonlocal properties of two-qubit gates and mixed states, and the optimization of quantum computations. Quant. Info. Proc. 1, 243 (2002)","journal-title":"Quant. Info. Proc."},{"key":"77_CR7","doi-asserted-by":"crossref","first-page":"052301","DOI":"10.1103\/PhysRevA.67.052301","volume":"67","author":"M.A. Nielsen","year":"2003","unstructured":"Nielsen M.A. et al.: Quantum dynamics as a physical resource. Phys. Rev. A 67, 052301 (2003)","journal-title":"Phys. Rev. A"},{"key":"77_CR8","doi-asserted-by":"crossref","first-page":"057901","DOI":"10.1103\/PhysRevLett.89.057901","volume":"89","author":"W. D\u00fcr","year":"2002","unstructured":"D\u00fcr W., Vidal G., Cirac J.I.: Optimal conversion of nonlocal unitary operations. Phys. Rev. Lett. 89, 057901 (2002)","journal-title":"Phys. Rev. Lett."},{"key":"77_CR9","doi-asserted-by":"crossref","first-page":"9463","DOI":"10.1088\/1751-8113\/40\/31\/021","volume":"40","author":"M.W. Coffey","year":"2007","unstructured":"Coffey M.W., Colburn G.G.: Feasibility of the controlled-NOT gate from certain model Hamiltonians. J. Phys. A 40, 9463 (2007)","journal-title":"J. Phys. A"},{"key":"77_CR10","doi-asserted-by":"crossref","unstructured":"Coffey, M.W., Deiotte, R., Semi, T.: Comment on \u201cUniversal quantum circuit for two-qubit transformations with three controlled-NOT gates\u201d and \u201cRecognizing small-circuit structure in two-qubit operators\u201d. Phys. Rev. A 77 (2008), to appear","DOI":"10.1103\/PhysRevA.77.066301"},{"key":"77_CR11","doi-asserted-by":"crossref","unstructured":"Tyson, J.E.: Operator-Schmidt decompositions and the Fourier transform, with applications to the operator-Schmidt numbers of unitaries. J. Phys. A 36, 10101, ibid. 36, 6813 (2003)","DOI":"10.1088\/0305-4470\/36\/39\/309"},{"key":"77_CR12","doi-asserted-by":"crossref","first-page":"052323","DOI":"10.1103\/PhysRevA.72.052323","volume":"72","author":"H. Fan","year":"2005","unstructured":"Fan H., Roychowdhury V., Szkopek T.: Optimal two-qubit quantum circuits using exchange interactions. Phys. Rev. A 72, 052323 (2005)","journal-title":"Phys. Rev. A"},{"key":"77_CR13","doi-asserted-by":"crossref","first-page":"052311","DOI":"10.1103\/PhysRevA.68.052311","volume":"68","author":"A.M. Childs","year":"2003","unstructured":"Childs A.M., Haselgrove H.L., Nielsen M.A.: Lower bounds on the complexity of simulating quantum gates. Phys. Rev. A 68, 052311 (2003)","journal-title":"Phys. Rev. A"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-008-0077-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11128-008-0077-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-008-0077-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T03:36:26Z","timestamp":1559360186000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11128-008-0077-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,6]]},"references-count":13,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[2008,6]]}},"alternative-id":["77"],"URL":"https:\/\/doi.org\/10.1007\/s11128-008-0077-6","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"value":"1570-0755","type":"print"},{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,6]]}}}