@article(Abbott2018CommunicationChannels,
 author       = {Alastair A. Abbott and Julian Wechs and Dominic Horsman and Mehdi Mhalla and Cyril Branciard},
 year         = {2020},
 title        = {{Communication through coherent control of quantum channels}},
 journal      = {Quantum},
 volume       = {4},
 pages        = {333},
 doi          = {10.22331/Q-2020-09-24-333},
)
@inproceedings(Abramsky2004AProtocols,
 author       = {Samson Abramsky and Bob Coecke},
 year         = {2004},
 title        = {{A categorical semantics of quantum protocols}},
 booktitle    = {Proceedings - Symposium on Logic in Computer Science},
 volume       = {19},
 pages        = {415--425},
 doi          = {10.1109/lics.2004.1319636},
)
@article(Adamyk2017SORTINGCYCLES,
 author       = {K. L.M. Adamyk and E. Holmes and G. R. Mayfield and D. J. Moritz and M. Scheepers and B. E. Tenner and H. C. Wauck},
 year         = {2017},
 title        = {{Sorting permutations: Games, genomes, and cycles}},
 journal      = {Discrete Mathematics, Algorithms and Applications},
 volume       = {9},
 number       = {5},
 doi          = {10.1142/S179383091750063X},
)
@article(Araujo2014ComputationalGates,
 author       = {Mateus Ara{\'{u}}jo and Fabio Costa and \begingroup\let \relax\relax \endgroup[Pleaseinsert\PrerenderUnicode{Č}intopreamble]aslav Brukner},
 year         = {2014},
 title        = {{Computational advantage from quantum-controlled ordering of gates}},
 journal      = {Physical Review Letters},
 volume       = {113},
 number       = {25},
 pages        = {250402},
 doi          = {10.1103/PhysRevLett.113.250402},
)
@article(Boixo2012EntangledDephasing,
 author       = {Sergio Boixo and Chris Heunen},
 year         = {2012},
 title        = {{Entangled and sequential quantum protocols with dephasing}},
 journal      = {Physical Review Letters},
 volume       = {108},
 number       = {12},
 pages        = {120402},
 doi          = {10.1103/PhysRevLett.108.120402},
)
@article(Chancellor2016GraphicalCorrection,
 author       = {Nicholas Chancellor and Aleks Kissinger and Joschka Roffe and Stefan Zohren and Dominic Horsman},
 year         = {2016},
 title        = {Graphical Structures for Design and Verification of Quantum Error Correction},
 journal      = {arXiv:\href{http://arxiv.org/abs/21611.08012}{21611.08012}},
)
@article(Chiribella2008TransformingSupermaps,
 author       = {G. Chiribella and G. M. D'Ariano and P. Perinotti},
 year         = {2008},
 title        = {{Transforming quantum operations: Quantum supermaps}},
 journal      = {EPL (Europhysics Letters)},
 volume       = {83},
 number       = {3},
 pages        = {30004},
 doi          = {10.1209/0295-5075/83/30004},
)
@article(chiribella2009beyond,
 author       = {G Chiribella and D\begingroup\let \relax\relax \endgroup[Pleaseinsert\PrerenderUnicode{’}intopreamble]Ariano, GM and P Perinotti and B Valiron},
 year         = {2009},
 title        = {Beyond quantum computers},
 journal      = {arXiv:\href{http://arxiv.org/abs/0912.0195}{0912.0195}},
)
@article(Chiribella2012PerfectStructures,
 author       = {Giulio Chiribella},
 year         = {2012},
 title        = {{Perfect discrimination of no-signalling channels via quantum superposition of causal structures}},
 journal      = {Physical Review A - Atomic, Molecular, and Optical Physics},
 volume       = {86},
 number       = {4},
 pages        = {040301},
 doi          = {10.1103/PhysRevA.86.040301},
)
@article(Chiribella2018IndefiniteChannel,
 author       = {Giulio Chiribella and Manik Banik and Some Sankar Bhattacharya and Tamal Guha and Mir Alimuddin and Arup Roy and Sutapa Saha and Sristy Agrawal and Guruprasad Kar},
 year         = {2018},
 title        = {Indefinite causal order enables perfect quantum communication with zero capacity channel},
 journal      = {arXiv:\href{http://arxiv.org/abs/1810.10457}{1810.10457}},
)
@article(chiribella2009theoretical,
 author       = {Giulio Chiribella and Giacomo Mauro D'Ariano and Paolo Perinotti},
 year         = {2009},
 title        = {Theoretical framework for quantum networks},
 journal      = {Phys. Rev. A},
 volume       = {80},
 pages        = {022339},
 doi          = {10.1103/PhysRevA.80.022339},
)
@article(Chiribella2013QuantumStructure,
 author       = {Giulio Chiribella and Giacomo Mauro D'Ariano and Paolo Perinotti and Benoit Valiron},
 year         = {2013},
 title        = {{Quantum computations without definite causal structure}},
 journal      = {Physical Review A - Atomic, Molecular, and Optical Physics},
 volume       = {88},
 number       = {2},
 pages        = {022318},
 doi          = {10.1103/PhysRevA.88.022318},
)
@article(chiribella2020quantumcomm,
 author       = {Giulio Chiribella and Matthew Wilson and H. F. Chau},
 year         = {2020},
 title        = {Quantum and Classical Data Transmission Through Completely Depolarising Channels in a Superposition of Cyclic Orders},
 journal      = {{2005.00618}},
)
@article(Coecke2008AxiomaticCPM-construction,
 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},
 number       = {C},
 pages        = {3--13},
 doi          = {10.1016/j.entcs.2008.04.014},
)
@article(Coecke2010QuantumPicturalism,
 author       = {Bob Coecke},
 year         = {2010},
 title        = {{Quantum picturalism}},
 journal      = {Contemporary Physics},
 volume       = {51},
 number       = {1},
 pages        = {59--83},
 doi          = {10.1080/00107510903257624},
)
@article(Coecke2013CausalProcesses,
 author       = {Bob Coecke and Raymond Lal},
 year         = {2013},
 title        = {{Causal Categories: Relativistically Interacting Processes}},
 journal      = {Foundations of Physics},
 volume       = {43},
 number       = {4},
 pages        = {458--501},
 doi          = {10.1007/s10701-012-9646-8},
)
@article(colnaghi2012quantum,
 author       = {Timoteo Colnaghi and Giacomo Mauro D'Ariano and Stefano Facchini and Paolo Perinotti},
 year         = {2012},
 title        = {Quantum computation with programmable connections between gates},
 journal      = {Physics Letters A},
 volume       = {376},
 number       = {45},
 pages        = {2940--2943},
 doi          = {10.1016/j.physleta.2012.08.028},
)
@article(Ebler2018EnhancedOrder,
 author       = {Daniel Ebler and Sina Salek and Giulio Chiribella},
 year         = {2018},
 title        = {{Enhanced Communication with the Assistance of Indefinite Causal Order}},
 journal      = {Physical Review Letters},
 volume       = {120},
 number       = {12},
 pages        = {120502},
 doi          = {10.1103/PhysRevLett.120.120502},
)
@inproceedings(Facchini2015QuantumProblem,
 author       = {Stefano Facchini and Simon Perdrix},
 year         = {2015},
 title        = {{Quantum circuits for the unitary permutation problem}},
 booktitle    = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
 volume       = {9076},
 publisher    = {Springer Verlag},
 pages        = {324--331},
 doi          = {10.1007/978-3-319-17142-5{\_}28},
)
@article(Gogioso2017FullyProblem,
 author       = {Stefano Gogioso and Aleks Kissinger},
 year         = {2017},
 title        = {Fully graphical treatment of the quantum algorithm for the Hidden Subgroup Problem},
 journal      = {{1701.08669}},
)
@article(Guerin2016ExponentialCommunication,
 author       = {Philippe Allard Gu{\'{e}}rin and Adrien Feix and Mateus Ara{\'{u}}jo and \begingroup\let \relax\relax \endgroup[Pleaseinsert\PrerenderUnicode{Č}intopreamble]aslav Brukner},
 year         = {2016},
 title        = {{Exponential Communication Complexity Advantage from Quantum Superposition of the Direction of Communication}},
 journal      = {Physical Review Letters},
 volume       = {117},
 number       = {10},
 pages        = {100502},
 doi          = {10.1103/PhysRevLett.117.100502},
)
@article(Guerin2019CommunicationNoise,
 author       = {Philippe Allard Gu{\'{e}}rin and Giulia Rubino and \begingroup\let \relax\relax \endgroup[Pleaseinsert\PrerenderUnicode{Č}intopreamble]aslav Brukner},
 year         = {2019},
 title        = {{Communication through quantum-controlled noise}},
 journal      = {Physical Review A},
 volume       = {99},
 number       = {6},
 doi          = {10.1103/PhysRevA.99.062317},
)
@article(Holevo1998TheStatesb,
 author       = {A. S. Holevo},
 year         = {1998},
 title        = {{The capacity of the quantum channel with general signal states}},
 journal      = {IEEE Transactions on Information Theory},
 volume       = {44},
 number       = {1},
 pages        = {269--273},
 doi          = {10.1109/18.651037},
)
@article(Kissinger2017Picture-perfectDistribution,
 author       = {Aleks Kissinger and Sean Tull and Bas Westerbaan},
 year         = {2017},
 title        = {Picture-perfect Quantum Key Distribution},
 journal      = {{1704.08668}},
)
@article(Kissinger2019AStructure,
 author       = {Aleks Kissinger and Sander Uijlen},
 year         = {2019},
 title        = {{A categorical semantics for causal structure}},
 journal      = {Logical Methods in Computer Science},
 volume       = {15},
 number       = {3},
 doi          = {10.23638/LMCS-15(3:15)2019},
)
@article(Kristjansson2019ResourceProcesses,
 author       = {Hl\IeC{\'e}r Kristj{\'{a}}nsson and Giulio Chiribella and Sina Salek and Daniel Ebler and Matthew Wilson},
 year         = {2020},
 title        = {{Resource theories of communication}},
 journal      = {New Journal of Physics},
 volume       = {22},
 number       = {7},
 pages        = {073014},
 doi          = {10.1088/1367-2630/ab8ef7},
)
@article(Mukhopadhyay2018SuperpositionThermometry,
 author       = {Chiranjib Mukhopadhyay and Manish K. Gupta and Arun Kumar Pati},
 year         = {2018},
 title        = {Superposition of causal order as a metrological resource for quantum thermometry},
 journal      = {{1812.07508}},
)
@article(Oreshkov2012QuantumOrder,
 author       = {Ognyan Oreshkov and Fabio Costa and \begingroup\let \relax\relax \endgroup[Pleaseinsert\PrerenderUnicode{Č}intopreamble]aslav Brukner},
 year         = {2012},
 title        = {{Quantum correlations with no causal order}},
 journal      = {Nature Communications},
 volume       = {3},
 doi          = {10.1038/ncomms2076},
)
@article(Procopio2019CommunicationScenario,
 author       = {Lorenzo M. Procopio and Francisco Delgado and Marco Enr{\'{i}}quez and Nadia Belabas and Juan Ariel Levenson},
 year         = {2019},
 title        = {{Communication Enhancement through Quantum Coherent Control of N Channels in an Indefinite Causal-Order Scenario}},
 journal      = {Entropy},
 volume       = {21},
 number       = {10},
 pages        = {1012},
 doi          = {10.3390/e21101012},
)
@article(Procopio2020SendingOrders,
 author       = {Lorenzo M. Procopio and Francisco Delgado and Marco Enr{\'{i}}quez and Nadia Belabas and Juan Ariel Levenson},
 year         = {2020},
 title        = {{Sending classical information via three noisy channels in superposition of causal orders}},
 journal      = {Physical Review A},
 volume       = {101},
 number       = {1},
 pages        = {012346},
 doi          = {10.1103/PhysRevA.101.012346},
)
@article(Ranchin2014CompleteMechanics,
 author       = {Andr\IeC{\'e} Ranchin and Bob Coecke},
 year         = {2014},
 title        = {{Complete set of circuit equations for stabilizer quantum mechanics}},
 journal      = {Physical Review A - Atomic, Molecular, and Optical Physics},
 volume       = {90},
 number       = {1},
 pages        = {012109},
 doi          = {10.1103/PhysRevA.90.012109},
)
@article(Salek2018QuantumOrders,
 author       = {Sina Salek and Daniel Ebler and Giulio Chiribella},
 year         = {2018},
 title        = {Quantum communication in a superposition of causal orders},
 journal      = {{1809.06655}},
)
@article(sazim2020classical,
 author       = {Sk Sazim and Kratveer Singh and Arun Kumar Pati},
 year         = {2020},
 title        = {Classical Communications with Indefinite Causal Order for $N$ completely depolarizing channels},
 journal      = {{2004.14339}},
)
@article(Schumacher1995QuantumCoding,
 author       = {Benjamin Schumacher},
 year         = {1995},
 title        = {{Quantum coding}},
 journal      = {Physical Review A},
 volume       = {51},
 number       = {4},
 pages        = {2738--2747},
 doi          = {10.1103/PhysRevA.51.2738},
)
@article(Selinger2007DaggerAbstract,
 author       = {Peter Selinger},
 year         = {2007},
 title        = {{Dagger Compact Closed Categories and Completely Positive Maps. (Extended Abstract)}},
 journal      = {Electronic Notes in Theoretical Computer Science},
 volume       = {170},
 pages        = {139--163},
 doi          = {10.1016/j.entcs.2006.12.018},
)
@article(Vicary2012TheAlgorithms,
 author       = {Jamie Vicary},
 year         = {2012},
 title        = {{The Topology of Quantum Algorithms}},
 journal      = {Proceedings - Symposium on Logic in Computer Science},
 pages        = {93--102},
 doi          = {10.1109/LICS.2013.14},
)
@book(Wilde2013QuantumTheory,
 author       = {Mark M. Wilde},
 year         = {2013},
 title        = {{Quantum Information Theory}},
 publisher    = {Cambridge University Press},
 address      = {Cambridge},
 doi          = {10.1017/CBO9781139525343},
)
@inproceedings(Zeng2014AbstractAlgorithms,
 author       = {William Zeng and Jamie Vicary},
 year         = {2014},
 title        = {{Abstract structure of unitary oracles for quantum algorithms}},
 booktitle    = {Electronic Proceedings in Theoretical Computer Science, EPTCS},
 volume       = {172},
 publisher    = {Open Publishing Association},
 pages        = {270--284},
 doi          = {10.4204/EPTCS.172.19},
)
@article(zhao2019quantum,
 author       = {Xiaobin Zhao and Yuxiang Yang and Giulio Chiribella},
 year         = {2020},
 title        = {{Quantum Metrology with Indefinite Causal Order}},
 journal      = {Physical Review Letters},
 volume       = {124},
 number       = {19},
 pages        = {190503},
 doi          = {10.1103/PhysRevLett.124.190503},
)