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thesis.bib
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% References by William J. Zeng
% Spring 2015
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% ZENG PAPERS
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@ARTICLE{gogioso2015fourier,
AUTHOR = "S. Gogioso and W. Zeng",
TITLE = "Fourier transforms from strongly complementary observables",
YEAR = "2015",
journal = {arXiv preprint arXiv:1501.04995}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% OVERVIEW
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article{hardy2001quantum,
title={Quantum theory from five reasonable axioms},
author={Hardy, Lucien},
journal={arXiv preprint quant-ph/0101012},
year={2001}
}
@article{chiribella2011informational,
title={Informational derivation of quantum theory},
author={Chiribella, Giulio and D’Ariano, Giacomo Mauro and Perinotti, Paolo},
journal={Physical Review A},
volume={84},
number={1},
pages={012311},
year={2011},
publisher={APS}
}
@inproceedings{green2013quipper,
title={Quipper: a scalable quantum programming language},
author={Green, Alexander S and Lumsdaine, Peter LeFanu and Ross, Neil J and Selinger, Peter and Valiron, Beno{\^\i}t},
booktitle={ACM SIGPLAN Notices},
volume={48},
number={6},
pages={333--342},
year={2013},
organization={ACM}
}
@article{wecker2014liqui,
title={{L}I{Q}Ui$|\rangle$: A Software Design Architecture and Domain-Specific Language for Quantum Computing},
author={Wecker, Dave and Svore, Krysta M},
journal={arXiv preprint arXiv:1402.4467},
year={2014}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Diagrams and Categories &
% Abstract Process Theories
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article{coecke2011interacting,
title={Interacting quantum observables: categorical algebra and diagrammatics},
author={Coecke, Bob and Duncan, Ross},
journal={New Journal of Physics},
volume={13},
number={4},
pages={043016},
year={2011},
publisher={IOP Publishing}
}
@book{cqm-notes,
author = {Chris Heunen and Jamie Vicary},
title = {Categories for Quantum Theory: An Introduction},
publisher = {Oxford University Press},
year = {to appear 2015}
}
@book{qcs-notes,
author = {Bob Coecke and Aleks Kissinger},
title = {Picturing Quantum Processes},
year = {to appear 2015},
publisher = {Cambridge University Press}
}
@article{joyal1993braided,
title={Braided tensor categories},
author={Joyal, Andr{\'e} and Street, Ross},
journal={Advances in Mathematics},
volume={102},
number={1},
pages={20--78},
year={1993},
publisher={Elsevier}
}
@inproceedings{mac1969one,
title={One universe as a foundation for category theory},
author={Mac Lane, Saunders},
booktitle={Reports of the Midwest Category Seminar III},
pages={192--200},
year={1969},
organization={Springer}
}
@incollection{selinger2011survey,
title={A survey of graphical languages for monoidal categories},
author={Selinger, Peter},
booktitle={New structures for physics},
pages={289--355},
year={2011},
publisher={Springer}
}
@article{joyal1991geometry,
title={The geometry of tensor calculus, I},
author={Joyal, Andr{\'e} and Street, Ross},
journal={Advances in Mathematics},
volume={88},
number={1},
pages={55--112},
year={1991},
publisher={Elsevier}
}
@article{kelly1980coherence,
title={Coherence for compact closed categories},
author={Kelly, Gregory M and Laplaza, Miguel L},
journal={Journal of Pure and Applied Algebra},
volume={19},
pages={193--213},
year={1980},
publisher={Elsevier}
}
@inproceedings{abramsky2004categorical,
title={A categorical semantics of quantum protocols},
author={Abramsky, Samson and Coecke, Bob},
booktitle={Logic in Computer Science, 2004. Proceedings of the 19th Annual IEEE Symposium on},
pages={415--425},
year={2004},
organization={IEEE}
}
@article{vicary2011completeness,
title={Completeness of†-categories and the complex numbers},
author={Vicary, Jamie},
journal={Journal of Mathematical Physics},
volume={52},
number={8},
pages={082104},
year={2011},
publisher={AIP Publishing}
}
@article{coecke2013new,
title={A new description of orthogonal bases},
author={Coecke, Bob and Pavlovic, Dusko and Vicary, Jamie},
journal={Mathematical Structures in Computer Science},
volume={23},
number={03},
pages={555--567},
year={2013},
publisher={Cambridge Univ Press}
}
@article{abramsky2012h,
title={H*-algebras and nonunital {F}robenius algebras: first steps in infinite-dimensional categorical quantum mechanics},
author={Abramsky, Samson and Heunen, Chris},
journal={Clifford Lectures},
volume={71},
pages={1--24},
year={2012}
}
@article{maclane1963natural,
title={Natural associativity and commutativity},
author={MacLane, Saunders},
year={1963},
publisher={Electronic version published by Fondren Library, Rice University, made possible with funding from the Rice Historical Society and Thomas R. Williams, Ph. D., class of 2000.}
}
@article{penrose1971applications,
title={Applications of negative dimensional tensors},
author={Penrose, Roger},
journal={Combinatorial mathematics and its applications},
volume={221244},
year={1971}
}
@article{baez2009prehistory,
title={A prehistory of n-categorical physics},
author={Baez, John C and Lauda, Aaron},
journal={Deep Beauty: Understanding the Quantum World Through Mathematical Innovation},
pages={13--128},
year={2009}
}
@article{reshetikhin1990ribbon,
title={Ribbon graphs and their invaraints derived from quantum groups},
author={Reshetikhin, Nicolai Yu and Turaev, Vladimir G},
journal={Communications in Mathematical Physics},
volume={127},
number={1},
pages={1--26},
year={1990},
publisher={Springer}
}
@article{atiyah1988topological,
title={Topological quantum field theory},
author={Atiyah, Michael F},
journal={Publications Math{\'e}matiques de l'IH{\'E}S},
volume={68},
pages={175--186},
year={1988}
}
@article{abrams1996two,
title={Two-dimensional topological quantum field theories and {F}robenius algebras},
author={Abrams, Lowell},
journal={Journal of Knot Theory and its Ramifications},
volume={5},
number={05},
pages={569--587},
year={1996},
publisher={World Scientific}
}
@book{kock2004frobenius,
title={{F}robenius algebras and 2-d topological quantum field theories},
author={Kock, Joachim},
volume={59},
year={2004},
publisher={Cambridge University Press}
}
@book{baez2011physics,
title={Physics, topology, logic and computation: a {R}osetta {S}tone},
author={Baez, John and Stay, Mike},
year={2011},
publisher={Springer}
}
@incollection{abramsky2008petri,
title={Petri nets, discrete physics, and distributed quantum computation},
author={Abramsky, Samson},
booktitle={Concurrency, Graphs and Models},
pages={527--543},
year={2008},
publisher={Springer}
}
@article{sassone1998axiomatization,
title={An axiomatization of the category of Petri net computations},
author={Sassone, Vladimiro},
journal={Mathematical Structures in Computer Science},
volume={8},
number={02},
pages={117--151},
year={1998},
publisher={Cambridge Univ Press}
}
@inproceedings{marti1989petri,
title={From Petri nets to linear logic},
author={Mart{\'\i}-Oliet, Narciso and Meseguer, Jos{\'e}},
booktitle={Category Theory and Computer Science},
pages={313--340},
year={1989},
organization={Springer}
}
@article{meseguer1990petri,
title={Petri nets are monoids},
author={Meseguer, Jos{\'e} and Montanari, Ugo},
journal={Information and computation},
volume={88},
number={2},
pages={105--155},
year={1990},
publisher={Elsevier}
}
@misc{petriBlog,
author = {Gopalkrishnan, Manoj},
title = {Autocatalysis in Reaction Networks},
journal = {Azimuth},
type = {Blog},
number = {October 11},
year = {2013},
howpublished = {\url{https://johncarlosbaez.wordpress.com/2013/10/11/autocatalysis-in-reaction-networks/}}
}
@article{baez2014categories,
title={Categories in control},
author={Baez, John C and Erbele, Jason},
journal={Theory and Applications of Categories},
volume={30},
pages={836--881},
number={24},
eprint={arXiv:1405.6881 [math.CT]},
year={2015}
}
@inproceedings{bonchi2015full,
title={Full abstraction for signal flow graphs},
author={Bonchi, Filippo and Sobocinski, Pawel and Zanasi, Fabio},
booktitle={Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages},
pages={515--526},
year={2015},
organization={ACM}
}
@article{baez2015compositional,
title={A compositional framework for passive linear networks},
author={Baez, John C and Fong, Brendan},
journal={arXiv preprint arXiv:1504.05625},
year={2015}
}
@incollection{mellies2014local,
title={Local states in string diagrams},
author={Mellies, Paul-Andr{\'e}},
booktitle={Rewriting and Typed Lambda Calculi},
pages={334--348},
year={2014},
publisher={Springer}
}
@inproceedings{grov2014tinker,
title={Tinker, tailor, solver, proof},
author={Grov, Gudmund and Kissinger, Aleks and Lin, Yuhui},
booktitle={UITP 2014},
journal={EPTCS},
year={2014},
pages={23--34},
}
@incollection{michaelson2012reasoning,
title={Reasoning about multi-process systems with the box calculus},
author={Michaelson, Greg and Grov, Gudmund},
booktitle={Central European Functional Programming School},
pages={279--338},
year={2012},
publisher={Springer}
}
@incollection{coecke2011categories,
title={Categories for the practising physicist},
author={Coecke, Bob and Paquette, {\'E}ric Oliver},
booktitle={New Structures for Physics},
pages={173--286},
year={2011},
publisher={Springer}
}
@article{abramsky2012operational,
title={Operational theories and Categorical quantum mechanics},
author={Abramsky, Samson and Heunen, Chris},
journal={arXiv preprint arXiv:1206.0921},
year={2012}
}
@article{bonchi2014interacting,
title={Interacting {H}opf Algebras},
author={Bonchi, Filippo and Sobocinski, Pawel and Zanasi, Fabio},
journal={arXiv preprint arXiv:1403.7048},
year={2014}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Generalized Compositional Theories
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article{coecke2015generalised,
title={Generalised Compositional Theories and Diagrammatic Reasoning},
author={Coecke, Bob and Duncan, Ross and Kissinger, Aleks and Wang, Quanlong},
journal={arXiv preprint arXiv:1506.03632},
year={2015}
}
@article{selinger2007dagger,
title={Dagger compact closed categories and completely positive maps},
author={Selinger, Peter},
journal={Electronic Notes in Theoretical Computer Science},
volume={170},
pages={139--163},
year={2007},
publisher={Elsevier}
}
@inproceedings{coecke2012strong,
title={Strong complementarity and non-locality in categorical quantum mechanics},
author={Coecke, Bob and Duncan, Ross and Kissinger, Aleks and Wang, Quanlong},
booktitle={Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science},
pages={245--254},
year={2012},
organization={IEEE Computer Society}
}
@MastersThesis{katriel-commitment,
author = {Katriel Cohn-Gordon},
title = {Commitment Algorithms},
school = {Department of Computer Science, University of Oxford},
year = 2012,
url = {http://www.cs.ox.ac.uk/people/bob.coecke/Katriel}
}
@book{kelly1982basic,
title={Basic concepts of enriched category theory},
author={Kelly, Gregory Maxwell},
number={64},
year={1982},
publisher={CUP Archive}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Strong Complementarity and Fourier Transform
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book{rudin1962fourier,
title={Fourier analysis on groups},
author={Rudin, Walter},
number={12},
year={1962},
publisher={Wiley}
}
@incollection{cartier2007primer,
title={A primer of {H}opf algebras},
author={Cartier, Pierre},
booktitle={Frontiers in Number Theory, Physics, and Geometry II},
pages={537--615},
year={2007},
publisher={Springer}
}
@book{street2007quantum,
title={Quantum Groups: a path to current algebra},
author={Street, Ross},
volume={19},
year={2007},
publisher={Cambridge University Press}
}
@article{abramsky2008categorical,
title={Categorical quantum mechanics},
author={Abramsky, Samson and Coecke, Bob},
journal={Handbook of quantum logic and quantum structures: quantum logic},
pages={261--324},
year={2008}
}
@book{nielsen2010quantum,
title={Quantum computation and quantum information},
author={Nielsen, Michael A and Chuang, Isaac L},
year={2010},
publisher={Cambridge university press}
}
@article{gogioso2015mermin,
title={Mermin Non-Locality in Abstract Process Theories},
author={Gogioso, Stefano and Zeng, William},
journal={arXiv preprint arXiv:1506.02675},
year={2015}
}
@phdthesis{zamdzhiev2012abstract,
title={An abstract approach towards quantum secret sharing},
author={Zamdzhiev, Vladimir Nikolaev},
year={2012},
school={University of Oxford}
}
@ARTICLE{zeng2014abstract,
KEY = "CQM-AbstractStructureUnitaryOracles",
AUTHOR = "W. Zeng and J. Vicary",
TITLE = "Abstract structure of unitary oracles for quantum algorithms",
JOURNAL = "EPTCS 172",
YEAR = "2014",
DOI = "10.4204/EPTCS.172.19",
URL = "http://arxiv.org/abs/1209.3917"
}
@article{zeng2015models,
title={Models of Quantum Algorithms in Sets and Relations},
author={Zeng, William},
journal={arXiv preprint arXiv:1503.05857},
year={2015}
}
@InBook{pavlovic2009quantum,
author = {Dusko Pavlovic},
editor = {P. Bruza et. al},
title = {Third International symposium on Quantum Interaction},
chapter = {Quantum and classical structures in nondeterministic computation},
pages = {143-157},
publisher = {Springer},
year = 2009,
volume = 5494,
series = {Lecture Notes in Artifical Intelligence}
}
@article{aaronson2014need,
title={The need for structure in quantum speedups},
author={Aaronson, Scott and Ambainis, Andris},
journal={Theory of Computing},
volume={10},
number={6},
pages={133--166},
doi = {10.4086/toc.2014.v010a006},
year={2014},
url = {arXiv:quant-ph/0911.0996}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Quantum Blackbox Algorithms
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@inproceedings{vicary-tqa,
title={Topological Structure of Quantum Algorithms},
author={Vicary, Jamie},
booktitle={Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science},
pages={93--102},
year={2013},
organization={IEEE Computer Society}
}
@article{cleve1998quantum,
title={Quantum algorithms revisited},
author={Cleve, Richard and Ekert, Artur and Macchiavello, Chiara and Mosca, Michele},
journal={Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences},
volume={454},
number={1969},
pages={339--354},
year={1998},
publisher={The Royal Society}
}
@article{hoyer1999conjugated,
title={Conjugated operators in quantum algorithms},
author={H{\o}yer, Peter},
journal={Physical Review A},
volume={59},
number={5},
pages={3280},
year={1999},
publisher={APS}
}
@article{batty2006extending,
title={Extending the Promise of the {D}eutsch--{J}ozsa--{H}{\o}yer Algorithm for Finite Groups},
author={Batty, Michael and Duncan, Andrew J and Braunstein, Samuel L},
journal={LMS Journal of Computation and Mathematics},
volume={9},
pages={40--63},
year={2006},
publisher={Cambridge Univ Press}
}
@inproceedings{bernstein1993quantum,
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Mermin Nonlocality
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% QAlgDisCo
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% QAlg Relations
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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