Samson Abramsky & Bob Coecke (2003):
Physical traces: Quantum vs. classical information processing.
In: Electronic Notes in Theoretical Computer Science 69.
Elsevier B.V.,
pp. 1–22,
doi:10.1016/S1571-0661(04)80556-5.
Samson Abramsky & Bob Coecke (2004):
A categorical semantics of quantum protocols.
In: Proceedings - Symposium on Logic in Computer Science 19,
pp. 415–425,
doi:10.1109/lics.2004.1319636.
Huzihiro Araki (1980):
On a characterization of the state space of quantum mechanics.
Communications in Mathematical Physics 75(1),
pp. 1–24,
doi:10.1007/BF01609054.
Howard Barnum, Jonathan Barrett, Matthew Leifer & Alexander Wilce (2007):
Generalized no-broadcasting theorem.
Physical Review Letters 99(24),
pp. 240501,
doi:10.1007/BF00690066.
Jessica Bavaresco, Mio Murao & Marco Túlio Quintino (2020):
Strict hierarchy between parallel, sequential, and indefinite-causal-order strategies for channel discrimination.
arXiv preprint arXiv:2011.08300.
Available at http://arxiv.org/abs/2011.08300.
Jessica Bavaresco, Mio Murao & Marco Túlio Quintino (2021):
Unitary channel discrimination beyond group structures: Advantages of sequential and indefinite-causal-order strategies.
arXiv preprint arXiv:2105.13369.
Available at http://arxiv.org/abs/2105.13369.
Alessandro Bisio, Giulio Chiribella, Giacomo Mauro D\begingroupłet [Pleaseinsert\PrerenderUnicode’intopreamble]Ariano, Stefano Facchini & Paolo Perinotti (2010):
Optimal quantum learning of a unitary transformation.
Physical Review A 81(3),
pp. 032324,
doi:10.1142/S0219749906002018.
Alessandro Bisio, Giulio Chiribella, Giacomo Mauro D\begingroupłet [Pleaseinsert\PrerenderUnicode’intopreamble]Ariano & Paolo Perinotti (2010):
Information-disturbance tradeoff in estimating a unitary transformation.
Physical Review A 82(6),
pp. 062305,
doi:10.1103/PhysRevA.72.042338.
Titouan Carette, Marc De Visme & Simon Perdrix (2021):
Graphical Language with Delayed Trace: Picturing Quantum Computing with Finite Memory.
arXiv preprint arXiv:2102.03133v2.
G Chiribella, G M D'ariano & P Perinotti (2008):
Transforming quantum operations: Quantum supermaps.
EPL 83,
pp. 30004,
doi:10.1209/0295-5075/83/30004.
Available at www.epljournal.org.
Giulio Chiribella (2012):
Perfect discrimination of no-signalling channels via quantum superposition of causal structures.
Physical Review A (Rapid Communication) 86(4),
pp. 040301,
doi:10.1103/PhysRevA.86.040301.
Giulio Chiribella, Manik Banik, Some Sankar Bhattacharya, Tamal Guha, Mir Alimuddin, Arup Roy, Sutapa Saha, Sristy Agrawal & Guruprasad Kar (2021):
Indefinite causal order enables perfect quantum communication with zero capacity channels.
New Journal of Physics,
doi:10.1088/1367-2630/abe7a0.
Available at https://iopscience.iop.org/article/10.1088/1367-2630/abe7a0.
Giulio Chiribella, Giacomo Mauro D'Ariano, Paolo Perinotti & Benoit Valiron (2013):
Quantum computations without definite causal structure.
Physical Review A 88(2),
pp. 022318,
doi:10.1103/PhysRevA.88.022318.
Giulio Chiribella, Giacomo Mauro D\begingroupłet [Pleaseinsert\PrerenderUnicode’intopreamble]Ariano & Paolo Perinotti (2008):
Optimal cloning of unitary transformation.
Physical Review Letters 101(18),
pp. 180504,
doi:10.1103/PhysRevA.72.042338.
Giulio Chiribella, Giacomo Mauro D\begingroupłet [Pleaseinsert\PrerenderUnicode’intopreamble]Ariano & Paolo Perinotti (2009):
Theoretical framework for quantum networks.
Physical Review A 80(2),
pp. 022339,
doi:10.1103/PhysRevLett.99.240501.
Giulio Chiribella, Giacomo Mauro D\begingroupłet [Pleaseinsert\PrerenderUnicode’intopreamble]Ariano & Paolo Perinotti (2011):
Informational derivation of quantum theory.
Physical Review A 84(1),
pp. 012311,
doi:10.1103/PhysRevLett.103.170502.
Giulio Chiribella, Alessandro Toigo & Veronica Umanità (2013):
Normal completely positive maps on the space of quantum operations.
Open Systems & Information Dynamics 20(01),
pp. 1350003,
doi:10.1088/1751-8113/41/35/355302.
Giulio Chiribella, Matthew Wilson & H. F. Chau (2020):
Quantum and Classical Data Transmission Through Completely Depolarising Channels in a Superposition of Cyclic Orders.
arXiv preprint arXiv:2005.00618.
Available at http://arxiv.org/abs/2005.00618.
J R B Cockett & R A G Seely (1997):
Proof theory for full intuitionistic linear logic, bilinear logic, and mix categories.
Technical Report 5.
Robin Cockett, Cole Comfort & Priyaa Srinivasan (2018):
Dagger linear logic for categorical quantum mechanics.
arXiv preprint arXiv:1809.00275.
Available at http://arxiv.org/abs/1809.00275.
Robin Cockett & Priyaa V Srinivasan (2021):
Exponential modalities and complementarity.
arXiv preprint arXiv:2103.05191v1.
Bob Coecke (2010):
Quantum picturalism.
Contemporary Physics 51(1),
pp. 59–83,
doi:10.1080/00107510903257624.
Bob Coecke (2016):
Terminality implies no-signalling... and much more than that.
New Generation Computing 34(1-2),
pp. 69–85,
doi:10.1007/s00354-016-0201-6.
Bob Coecke, Bill Edwards & Robert W. Spekkens (2011):
Phase groups and the origin of non-locality for qubits.
In: Electronic Notes in Theoretical Computer Science 270.
Elsevier,
pp. 15–36,
doi:10.1016/j.entcs.2011.01.021.
Bob Coecke & Aleks Kissinger (2010):
The compositional structure of multipartite quantum entanglement.
In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 6199 LNCS.
Springer Verlag,
pp. 297–308,
doi:10.1007/978-3-642-14162-1_25.
Available at https://link.springer.com/chapter/10.1007/978-3-642-14162-1_25.
Bob Coecke & Raymond Lal (2012):
Time asymmetry of probabilities versus relativistic causal structure: An arrow of time.
Physical Review Letters 108(20),
doi:10.1103/PhysRevLett.108.200403.
Bob Coecke & Raymond Lal (2013):
Causal Categories: Relativistically Interacting Processes.
Foundations of Physics 43(4),
pp. 458–501,
doi:10.1007/s10701-012-9646-8.
Giacomo Mauro D'Ariano (2006):
How to Derive the Hilbert-Space Formulation of Quantum Mechanics From Purely Operational Axioms.
In: AIP Conference Proceedings 844.
AIP,
pp. 101–128,
doi:10.1063/1.2219356.
Qingxiuxiong Dong, Marco Túlio Quintino, Akihito Soeda & Mio Murao (2021):
The quantum switch is uniquely defined by its action on unitary operations.
arXiv preprint arXiv:2106.00034.
Available at https://arxiv.org/abs/2106.00034v2.
Thomas D Galley, Flaminia Giacomini & John H Selby:
A no-go theorem on the nature of the gravitational field beyond quantum theory.
arXiv preprint arXiv:2012.01441v1.
Stefano Gogioso & Fabrizio Genovese (2017):
Infinite-dimensional categorical quantum mechanics.
In: Electronic Proceedings in Theoretical Computer Science, EPTCS 236.
Open Publishing Association,
pp. 51–69,
doi:10.4204/EPTCS.236.4.
Stefano Gogioso & Fabrizio Genovese (2018):
Towards quantum field theory in categorical quantum mechanics.
In: Electronic Proceedings in Theoretical Computer Science, EPTCS 266.
Open Publishing Association,
pp. 349–366,
doi:10.4204/EPTCS.266.22.
Stefano Gogioso & Fabrizio Genovese (2019):
Quantum field theory in categorical quantum mechanics.
In: Electronic Proceedings in Theoretical Computer Science, EPTCS 287.
Open Publishing Association,
pp. 163–177,
doi:10.4204/EPTCS.287.9.
Gilad Gour & Carlo Maria Scandolo:
Dynamical Resources.
arXiv preprint arXiv:2101.01552v1.
Philippe Allard Guérin, Adrien Feix, Mateus Araújo & \begingroupłet [Pleaseinsert\PrerenderUnicodeČintopreamble]aslav Brukner (2016):
Exponential Communication Complexity Advantage from Quantum Superposition of the Direction of Communication.
Physical Review Letters 117(10),
pp. 100502,
doi:10.1103/PhysRevLett.117.100502.
Lucien Hardy (2001):
Quantum Theory From Five Reasonable Axioms.
arXiv preprint arXiv:quant-ph/0101012.
Available at http://arxiv.org/abs/quant-ph/0101012.
Lucien Hardy (2007):
Towards quantum gravity: a framework for probabilistic theories with non-fixed causal structure.
Journal of Physics A: Mathematical and Theoretical 40(12),
pp. 3081,
doi:10.1007/BF02105068.
Lucien Hardy (2021):
Time Symmetry in Operational Theories.
arXiv preprint arXiv:2104.00071v1.
Chris Heunen & Jamie Vicary (2019):
Categories for Quantum Theory.
Categories for Quantum Theory,
doi:10.1093/OSO/9780198739623.001.0001.
P. T. Johnstone (1983):
Basic Concepts of Enriched Category Theory (London Mathematical Society Lecture Note Series, 64).
Bulletin of the London Mathematical Society 15(1),
pp. 96–96,
doi:10.1112/blms/15.1.96.
Available at http://doi.wiley.com/10.1112/blms/15.1.96.
Aleks Kissinger & Sander Uijlen (2019):
A categorical semantics for causal structure.
Logical Methods in Computer Science 15(3),
doi:10.23638/LMCS-15(3:15)2019.
Hlér Kristjánsson, Giulio Chiribella, Sina Salek, Daniel Ebler & Matthew Wilson (2020):
Resource theories of communication.
New Journal of Physics 22(7),
pp. 073014,
doi:10.1088/1367-2630/ab8ef7.
Yunchao Liu & Xiao Yuan (2035):
Operational resource theory of quantum channels.
Physical Review Research 2,
doi:10.1103/PhysRevResearch.2.012035.
Zi-Wen Liu & Andreas Winter (2019):
Resource theories of quantum channels and the universal role of resource erasure.
arXiv preprint arXiv:1904.04201.
Available at https://arxiv.org/abs/1904.04201v1.
Giacomo Mauro D'Ariano, Giulio Chiribella & Paolo Perinotti (2017):
Quantum Theory from First Principles.
Cambridge University Press,
doi:10.1017/9781107338340.
Pau Enrique Moliner, Chris Heunen & Sean Tull (2017):
Space in Monoidal Categories.
In: Bob Coecke & Aleks Kissinger: Proceedings 14th International Conference on Quantum Physics and Logic, QPL 2017, Nijmegen, The Netherlands, 3-7 July 2017,
EPTCS 266,
pp. 399–410,
doi:10.4204/EPTCS.266.25.
Ognyan Oreshkov, Fabio Costa & \begingroupłet [Pleaseinsert\PrerenderUnicodeČintopreamble]aslav Brukner (2012):
Quantum correlations with no causal order.
Nature Communications 3,
doi:10.1038/ncomms2076.
Nicola Pinzani & Stefano Gogioso (2020):
Giving Operational Meaning to the Superposition of Causal Orders.
arXiv preprint arXiv:2003.13306.
Available at http://arxiv.org/abs/2003.13306.
Lorenzo M. Procopio, Francisco Delgado, Marco Enríquez, Nadia Belabas & Juan Ariel Levenson (2019):
Communication Enhancement through Quantum Coherent Control of N Channels in an Indefinite Causal-Order Scenario.
Entropy 21(10),
pp. 1012,
doi:10.3390/e21101012.
Available at https://www.mdpi.com/1099-4300/21/10/1012.
Lorenzo M. Procopio, Francisco Delgado, Marco Enríquez, Nadia Belabas & Juan Ariel Levenson (2020):
Sending classical information via three noisy channels in superposition of causal orders.
Physical Review A 101(1),
pp. 012346,
doi:10.1103/PhysRevA.101.012346.
Mario Román (2020):
Comb Diagrams for Discrete-Time Feedback.
arXiv preprint arXiv:2003.06214v1.
Mario Román (2020):
Open Diagrams via Coend Calculus.
In: David I. Spivak & Jamie Vicary: Proceedings of the 3rd Annual International Applied Category Theory Conference 2020, ACT 2020, Cambridge, USA, 6-10th July 2020,
EPTCS 333,
pp. 65–78,
doi:10.4204/EPTCS.333.5.
Sina Salek, Daniel Ebler & Giulio Chiribella (2018):
Quantum communication in a superposition of causal orders.
arXiv preprint arXiv:1809.06655.
Available at http://arxiv.org/abs/1809.06655.
David Schmid, John H Selby & Robert W Spekkens:
Unscrambling the omelette of causation and inference: The framework of causal-inferential theories.
arXiv preprint arXiv:2009.03297v2.
John H Selby & Ciarán M Lee (2020):
Compositional resource theories of coherence.
Technical Report,
doi:10.22331/q-2020-09-11-319.
John H. Selby, Carlo Maria Scandolo & Bob Coecke (2021):
Reconstructing quantum theory from diagrammatic postulates.
Quantum 5,
pp. 445,
doi:10.22331/q-2021-04-28-445.
Peter Selinger (2004):
Towards a quantum programming language.
Mathematical Structures in Computer Science 14(4),
pp. 527–586,
doi:10.1017/S0960129504004256.
Peter Selinger (2007):
Dagger Compact Closed Categories and Completely Positive Maps. (Extended Abstract).
Electronic Notes in Theoretical Computer Science 170,
pp. 139–163,
doi:10.1016/j.entcs.2006.12.018.
Peter Selinger & Beno\begingroupłet [Pleaseinsert\PrerenderUnicodeıintopreamble]t Valiron:
A Lambda Calculus for Quantum Computation with Classical Control.
Typed Lambda Calculi and Applications,
doi:10.1007/1141717026.
Julian Wechs, Hippolyte Dourdent, Alastair A Abbott & Cyril Branciard:
Quantum circuits with classical versus quantum control of causal order.
arXiv preprint arXiv:2101.08796v1.
Matthew Wilson & Giulio Chiribella (2020):
A Diagrammatic Approach to Information Transmission in Generalised Switches.
arXiv preprint arXiv:2003.08224.
Available at http://arxiv.org/abs/2003.08224.
William K Wootters (1990):
Local accessibility of quantum states.
Complexity, entropy and the physics of information 8,
pp. 39–46.
Margherita Zorzi (2016):
On quantum lambda calculi: a foundational perspective.
Mathematical Structures in Computer Science 26(7),
pp. 1107\begingroupłet [Pleaseinsert\PrerenderUnicode–intopreamble]1195,
doi:10.1017/S0960129514000425.