{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T04:35:03Z","timestamp":1781238903221,"version":"3.54.1"},"reference-count":20,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2009,4,1]],"date-time":"2009-04-01T00:00:00Z","timestamp":1238544000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100002855","name":"Ministry of Science and Technology of the People's Republic of China","doi-asserted-by":"publisher","award":["2007CB807901"],"award-info":[{"award-number":["2007CB807901"]}],"id":[{"id":"10.13039\/501100002855","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["6.07E+15"],"award-info":[{"award-number":["6.07E+15"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Comput. Logic"],"published-print":{"date-parts":[[2009,4]]},"abstract":"<jats:p>We introduce an algebra qCCS of pure quantum processes in which communications by moving quantum states physically are allowed and computations are modeled by super-operators, but no classical data is explicitly involved. An operational semantics of qCCS is presented in terms of (nonprobabilistic) labeled transition systems. Strong bisimulation between processes modeled in qCCS is defined, and its fundamental algebraic properties are established, including uniqueness of the solutions of recursive equations. To model sequential computation in qCCS, a reduction relation between processes is defined. By combining reduction relation and strong bisimulation we introduce the notion of strong reduction-bisimulation, which is a device for observing interaction of computation and communication in quantum systems. Finally, a notion of strong approximate bisimulation (equivalently, strong bisimulation distance) and its reduction counterpart are introduced. It is proved that both approximate bisimilarity and approximate reduction-bisimilarity are preserved by various constructors of quantum processes. This provides us with a formal tool for observing robustness of quantum processes against inaccuracy in the implementation of its elementary gates.<\/jats:p>","DOI":"10.1145\/1507244.1507249","type":"journal-article","created":{"date-parts":[[2009,4,15]],"date-time":"2009-04-15T13:37:07Z","timestamp":1239802627000},"page":"1-36","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":61,"title":["An algebra of quantum processes"],"prefix":"10.1145","volume":"10","author":[{"given":"Mingsheng","family":"Ying","sequence":"first","affiliation":[{"name":"Tsinghua University, Beijing, China and University of Technology, Sydney, Ultimo, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuan","family":"Feng","sequence":"additional","affiliation":[{"name":"Tsinghua University, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Runyao","family":"Duan","sequence":"additional","affiliation":[{"name":"Tsinghua University, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhengfeng","family":"Ji","sequence":"additional","affiliation":[{"name":"Institute of Software, Chinese Academy of Sciences, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2009,4,8]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/11539452_14"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.54.1844"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(82)90084-6"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2007.08.001"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/1040305.1040318"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129506005263"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/11527800_1"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/977091.977108"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2002.1097"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1070\/RM1997v052n06ABEH002155"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1017\/S096012950600524X"},{"key":"e_1_2_2_13_1","first-page":"109","article-title":"A process algebraic approach to concurrent and distributed quantum computation: Operational semantics. 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