@article(abramskyblutepanangaden:nuclearideals, author = "Samson Abramsky and Richard Blute and Prakhash Panangaden", year = "1999", title = "Nuclear and trace ideals in tensored *-categories", journal = "Journal of Pure and Applied Algebra", volume = "143", pages = "3--47", doi = "10.1016/S0022-4049(98)00106-6", ) @inproceedings(abramskycoecke:categoricalsemantics, author = "Samson Abramsky and Bob Coecke", year = "2004", title = "A categorical semantics of quantum protocols", booktitle = "Logic in Computer Science 19", publisher = "IEEE Computer Society", pages = "415--425", doi = "10.1109/LICS.2004.1319636", ) @techreport(coecke:mix, author = "Bob Coecke", year = "2007", title = "Complete positivity without positivity and without compactness", type = "Technical Report", number = "PRG-RR-07-05", institution = "Oxford University Computing Laboratory", url = "http://www.cs.ox.ac.uk/techreports/oucl/RR-07-05.html", ) @article(coecke:projective, author = "Bob Coecke", year = "2007", title = "De-linearizing Linearity: Projective Quantum Axiomatics From Strong Compact Closure", journal = "Electronic Notes in Theoretical Computer Science", volume = "170", pages = "49--72", doi = "10.1016/j.entcs.2006.12.011", ) @article(coecke:selinger, author = "Bob Coecke", year = "2008", title = "Axiomatic Description of Mixed States From Selinger's CPM-construction", journal = "Electronic Notes in Theoretical Computer Science", volume = "210", pages = "3--13", doi = "10.1016/j.entcs.2008.04.014", ) @inproceedings(coeckepaquette:naimark, author = "Bob Coecke and {\'E}ric O. Paquette", year = "2008", title = "POVMs and {N}aimark's theorem without sums", booktitle = "QPL IV", series = "ENTCS", volume = "210", pages = "15--31", doi = "10.1016/j.entcs.2008.04.015", ) @incollection(coeckepavlovic:classicalobjects, author = "Bob Coecke and Du{\v {s}}ko Pavlovi{\'c}", year = "2007", title = "Quantum measurements without sums", booktitle = "Mathematics of Quantum Computing and Technology", publisher = "Taylor and Francis", pages = "559--596", url = "arXiv:quant-ph/0608035", ) @inproceedings(coeckeperdrix:channels, author = "Bob Coecke and Simon Perdrix", year = "2010", title = "Environment and classical channels in categorical quantum mechanics", booktitle = "CSL'10/EACSL'10", publisher = "Springer", pages = "230--244", url = "http://dl.acm.org/citation.cfm?id=1887459.1887481", ) @book(conway:operatortheory, author = "John B. Conway", year = "2000", title = "A course in operator theory", publisher = "American Mathematical Society", ) @book(dixmier:vonneumann, author = "Jacques Dixmier", year = "1969", title = "Von {N}eumann algebras", publisher = "North-Holland", ) @article(heunen:compactlyaccessible, author = "Chris Heunen", year = "2008", title = "Compactly accessible categories and quantum key distribution", journal = "Logical Methods in Computer Science", volume = "4", number = "4", doi = "10.2168/LMCS-4(4:9)2008", ) @article(heunen:embedding, author = "Chris Heunen", year = "2009", title = "An embedding theorem for {H}ilbert categories", journal = "Theory and Applications of Categories", volume = "22", number = "13", pages = "321--344", url = "http://www.tac.mta.ca/tac/volumes/22/13/22-13abs.html", ) @inproceedings(heunenboixo:cpfrob, author = "Chris Heunen and Sergio Boixo", year = "2011", title = "Completely positive classical structures and sequentializable quantum protocols", booktitle = "QPL VIII", ) @book(holevo:statistical, author = "Alexander S. Holevo", year = "2001", title = "Statistical structure of quantum theory", publisher = "Springer", ) @article(joyalstreet:tensorcalculus, author = "A. Joyal and R. Street", year = "1991", title = "The geometry of tensor calculus {I}", journal = "Advances in Mathematics", volume = "88", pages = "55--112", doi = "10.1016/0001-8708(91)90003-P", ) @article(kellylaplaza:compactcategories, author = "G. Max Kelly and Miguel L. Laplaza", year = "1980", title = "Coherence for compact closed categories", journal = "Journal of Pure and Applied Algebra", volume = "19", pages = "193--213", doi = "10.1016/0022-4049(80)90101-2", ) @book(paulsen:completelypositive, author = "Vern Paulsen", year = "2002", title = "Completely bounded maps and operators algebras", publisher = "Cambridge University Press", ) @inproceedings(selinger:completelypositive, author = "Peter Selinger", year = "2007", title = "Dagger compact closed categories and completely positive maps", booktitle = "Quantum Programming Languages", series = "ENTCS", volume = "170", publisher = "Elsevier", pages = "139--163", doi = "10.1016/j.entcs.2006.12.018", ) @inproceedings(selinger:graphicallanguages, author = "Peter Selinger", year = "2010", title = "A survey of graphical languages for monoidal categories", booktitle = "New Structures for Physics", series = "Lecture Notes in Physics", volume = "813", publisher = "Springer", pages = "289--355", ) @article(stinespring:positive, author = "W. Forrest Stinespring", year = "1955", title = "Positive functions on {C}*-algebras", journal = "Proceedings of the American Mathematical Society", volume = "6", number = "2", pages = "211--216", ) @book(takesaki:operatoralgebras, author = "Masamichi Takesaki", year = "1979", title = "Theory of Operator Algebra I", series = "Encyclopaedia of Mathematical Sciences", publisher = "Springer", )