, Networked Quantum Information Technologies

A. A. Abbott, J. Wechs, D. Horsman, M. Mhalla, and C. Branciard, Communication through coherent control of quantum channels, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01927790

S. Abramsky and B. Coecke, A categorical semantics of quantum protocols, LICS, pp.415-425, 2004.

S. Abramsky and B. Coecke, A categorical semantics of quantum protocols, Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science (LICS), 2004.

M. Amy, J. Chen, and N. J. Ross, A finite presentation of CNOT-dihedral operators, Proceedings 14th International Conference on Quantum Physics and Logic, vol.266, pp.84-97, 2017.

P. Arrighi and S. Perdrix, Informatique Mathématique, une photographie en, 2016.

A. Aspect, J. Dalibard, and G. Roger, Experimental test of Bell's inequalities using time-varying analyzers, Phys. Rev. Lett, vol.49, issue.25, pp.1804-1807, 1982.

M. Backens, The ZX-calculus is complete for stabilizer quantum mechanics, Quantum Physics and Logic (QPL 2012), 2012.

M. Backens, The ZX-calculus is complete for the single-qubit Clifford+T group, Electronic Proceedings in Theoretical Computer Science, vol.172, pp.293-303, 2014.

M. Backens and A. Kissinger, ZH: A complete graphical calculus for quantum computations involving classical non-linearity, 2018.

M. Backens, S. Perdrix, and Q. Wang, A simplified stabilizer zx-calculus, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01404591

J. C. Baez and J. Erbele, Categories in control. Theory and Applications of Categories, vol.30, pp.836-881, 2015.

J. Bell, On the Einstein Podolsky Rosen paradox, Physics, vol.1, p.195, 1964.

C. H. Bennett and G. Brassard, Quantum cryptography: Public key distribution and coin tossing, Proceedings of IEEE international Conference on Computers, Systems and Signal Processing, p.175, 1984.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres et al., Wootters. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett, vol.70, pp.1895-1899, 1993.

C. H. Bennett and S. J. Wiesner, Communication via one-and two-particle operators on Einstein -Podolsky-Rosen states, Phys. Rev. Lett, vol.69, pp.2881-2884, 1992.

X. Bian and Q. Wang, Graphical calculus for qutrit systems, IEICE Transactions on Fundamentals of Electronics, vol.98, issue.1, pp.391-399, 2015.

F. Bonchi, P. Soboci?ski, and F. Zanasi, Interacting Hopf algebras, Journal of Pure and Applied Algebra, vol.221, issue.1, pp.144-184, 2017.

A. Bouchet, Connectivity of isotropic systems, Proceedings of the third international conference on Combinatorial mathematics, pp.81-93, 1989.

A. Broadbent, P. Chouha, and A. Tapp, The GHZ State in Secret Sharing and Entanglement Simulation, International Conference on Quantum, Nano, and Micro Technologies, 2009.

A. Broadbent, J. Fitzsimons, and E. Kashefi, Universal blind quantum computation, 50th Annual IEEE Symposium on Foundations of Computer Science, 2009.

A. Broadbent and E. Kashefi, Parallelizing quantum circuits, Theoretical Computer Science, vol.410, issue.26, pp.2489-2510, 2007.

D. E. Browne, E. Kashefi, M. Mhalla, and S. Perdrix, Generalized flow and determinism in measurement-based quantum computation, New Journal of Physics (NJP), vol.9, issue.8, 2007.

D. E. Browne, E. Kashefi, and S. Perdrix, Computational depth complexity of measurement-based quantum computation, Theory of Quantum Computation, Communication, and Cryptography (TQC'10), vol.6519, pp.35-46, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00932720

D. Cattanéo and S. Perdrix, Parameterized complexity of weak odd domination problems, Fundamentals of Computation Theory, pp.107-120, 2013.

D. Cattanéo and S. Perdrix, Minimum Degree up to Local Complementation: Bounds, Parameterized Complexity, and Exact Algorithms, 26th International Symposium on Algorithms and Computation, vol.9472, 2015.

M. Cesati, The turing way to parameterized complexity, Journal of Computer and System Sciences, vol.67, pp.654-685, 2003.

G. Chiribella, G. M. D'ariano, P. Perinotti, and B. Valiron, Quantum computations without definite causal structure, Physical Review A, vol.88, issue.2, p.22318, 2013.

B. Coecke and R. Duncan, Interacting quantum observables, ICALP (2), pp.298-310, 2008.

B. Coecke and B. Edwards, Three qubit entanglement within graphical Z/Xcalculus, 2011.

B. Coecke and A. Kissinger, The compositional structure of multipartite quantum entanglement, Automata, Languages and Programming, pp.297-308

B. Coecke and A. Kissinger, Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning, 2017.

B. Coecke, D. Pavlovic, and J. Vicary, A new description of orthogonal bases, Mathematical Structures in Computer Science, vol.23, issue.3, pp.555-567, 2013.

B. Coecke and S. Perdrix, Environment and classical channels in categorical quantum mechanics, Logical Methods in Computer Science, vol.8, issue.4, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00940885

V. Danos and E. Kashefi, Determinism in the one-way model, Physical Review A, vol.74, 2006.

V. Danos, E. Kashefi, and P. Panangaden, The measurement calculus, J. ACM, vol.54, issue.2, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00155304

V. Danos, E. Kashefi, P. Panangaden, and S. Perdrix, Extended Measurement Calculus, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00999645

N. De-beaudrap and D. Horsman, The ZX calculus is a language for surface code lattice surgery, 2017.

R. Downey, M. Fellows, A. Vardy, and G. Whittle, The parameterized complexity of some fundabmental problems in coding theory, CDMTCS Research Report Series, 1997.

R. Duncan and S. Perdrix, Graph states and the necessity of Euler decomposition, Conference on Computability in Europe, pp.167-177, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00940879

R. Duncan and S. Perdrix, Rewriting Measurement-Based Quantum Computations with Generalised Flow, International Colloquium on Automata, Languages and Programming (ICALP), pp.285-296, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00940895

R. Duncan and S. Perdrix, Pivoting makes the ZX-calculus complete for real stabilizers, QPL 2013, Electronic Proceedings in Theoretical Computer Science, pp.50-62, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00935185

D. Ebler, S. Salek, and G. Chiribella, Enhanced communication with the assistance of indefinite causal order, Physical review letters, vol.120, issue.12, p.120502, 2018.

A. Einstein, B. Podolsky, and N. Rosen, Can quantum-mechanical description of reality be considered complete?, Phys. Rev, vol.47, issue.10, pp.777-780, 1935.

S. Facchini and S. Perdrix, Quantum circuits for the unitary permutation problem, TAMC 2015, volume 9076 of Theory and Applications of Models of Computation, pp.324-331, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00994182

P. Golovach, J. Kratochvil, and O. Suchy, Parameterized complexity of generalized domination problems, Discrete Applied Mathematics, vol.160, pp.780-792, 2009.

D. Gottesman, Theory of quantum secret sharing, Phys. Rev. A, vol.61, p.42311, 2000.

S. Gravier, J. Javelle, M. Mhalla, and S. Perdrix, On weak odd domination and graph-based quantum secret sharing, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00944428

S. Gravier, J. Javelle, M. Mhalla, and S. Perdrix, Quantum secret sharing with graph states, Lecture Notes in Computer Science, vol.7721, pp.15-31, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00933722

A. S. Green, P. L. Lumsdaine, N. J. Ross, P. Selinger, and B. Valiron, Quipper: a scalable quantum programming language, ACM SIGPLAN Notices, vol.48, pp.333-342, 2013.

A. Hadzihasanovic, A diagrammatic axiomatisation for qubit entanglement, 30th Annual ACM/IEEE Symposium on Logic in Computer Science, pp.573-584, 2015.

A. Hadzihasanovic, The algebra of entanglement and the geometry of composition, 2017.

A. Hadzihasanovic, K. F. Ng, and Q. Wang, Two complete axiomatisations of pure-state qubit quantum computing, Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS '18, pp.502-511, 2018.

M. Hein, J. Eisert, and H. J. Briegel, Multiparty entanglement in graph states, Phys. Rev. A, vol.69, p.62311, 2004.

P. Høyer, M. Mhalla, and S. Perdrix, Resources required for preparing graph states, Proceedings of ISAAC06, vol.4288, pp.638-649, 2006.

P. Høyer and R. Spalek, Quantum fan-out is powerful, Theory of Computing, vol.1, issue.1, pp.81-103, 2005.

J. Javelle, M. Mhalla, and S. Perdrix, New protocols and lower bound for quantum secret sharing with graph states, Theory of Quantum Computation, Communication, and Cryptography (TQC'12), vol.09, p.2012

J. Javelle, M. Mhalla, and S. Perdrix, On the minimum degree up to local complementation: Bounds and complexity, Workshop on Graph-Theoretic Concepts in Computer Science (WG), 2012.
URL : https://hal.archives-ouvertes.fr/hal-00933720

E. , The rational fragment of the zx-calculus, 2018.

E. Jeandel, S. Perdrix, and R. Vilmart, Y-calculus: A language for real matrices derived from the zx-calculus, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01445948

E. Jeandel, S. Perdrix, and R. Vilmart, A complete axiomatisation of the ZXcalculus for Clifford+T quantum mechanics, Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS '18, pp.559-568, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01529623

E. Jeandel, S. Perdrix, and R. Vilmart, Diagrammatic reasoning beyond Clif-ford+T quantum mechanics, Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS '18, pp.569-578, 2018.

E. Jeandel, S. Perdrix, and R. Vilmart, A generic normal form for zxdiagrams and application to the rational angle completeness, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01791791

E. Jeandel, S. Perdrix, R. Vilmart, and Q. Wang, Generalised supplementarity and new rule for empty diagrams to make the zx-calculus more expressive, 2017.

E. Jeandel, S. Perdrix, R. Vilmart, and Q. Wang, ZX-calculus: Cyclotomic supplementarity and incompleteness for Clifford+T quantum mechanics, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017, vol.83, pp.1-11, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01445707

R. Jozsa, An introduction to measurement based quantum computation, 2005.

D. Kartsaklis, M. Sadrzadeh, S. Pulman, and B. Coecke, Reasoning about meaning in natural language with compact closed categories and Frobenius algebras. Logic and Algebraic Structures in Quantum Computing, p.199, 2013.

E. Kashefi, D. Markham, M. Mhalla, and S. Perdrix, Information flow in secret sharing protocols, vol.9, pp.87-97, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00940873

A. Keet, B. Fortescue, D. Markham, and B. C. Sanders, Quantum secret sharing with qudit graph states, Physical Review A, vol.82, p.62315, 2010.

A. Kotzig, Eulerian lines in finite 4-valent graphs and their transformations, Colloqium on Graph Theory, pp.219-230, 1968.

J. , Perfect codes in general graphs, 7th Hungarian colloqium on combinatorics, 1987.

A. Marin, D. Markham, and S. Perdrix, Access structure in graphs in high dimension and application to secret sharing, 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC'13) -to appear in LNCS, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00935108

D. Markham and B. C. Sanders, Graph states for quantum secret sharing, Physical Review A, vol.78, p.42309, 2008.

D. Markham and B. C. Sanders, Graph states for quantum secret sharing, Physical Review A, vol.78, p.42309, 2008.

K. Matsumoto and K. Amano, Representation of quantum circuits with Clifford and ?/8 gates, 2008.

M. Mhalla and S. Perdrix, Finding optimal flows efficiently, the 35th International Colloquium on Automata, Languages and Programming (ICALP), vol.5125, pp.857-868, 2008.

M. Mhalla and S. Perdrix, Graph states, pivot minor, and universality of (X,Z)-measurements, International Journal of Unconventional Computing (IJUC), 2012.
URL : https://hal.archives-ouvertes.fr/hal-00934104

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition, 2010.

S. Perdrix and Q. Wang, Supplementarity is necessary for quantum diagram reasoning, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016), vol.58, pp.1-76, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01361419

R. Prevedel, P. Walther, F. Tiefenbacher, P. Bohi, R. Kaltenbaek et al., High-speed linear optics quantum computing using active feed-forward, Nature, vol.445, issue.7123, pp.65-69, 2007.

R. Raussendorf and H. Briegel, A one-way quantum computer, Physical Review Letters, vol.86, issue.22, pp.5188-5191, 2001.

R. Raussendorf and H. Briegel, Computational model underlying the one-way quantum computer. Quantum Information and Computation, vol.6, p.433, 2002.

R. Raussendorf and H. J. Briegel, A one-way quantum computer, Phys. Rev. Lett, vol.86, pp.5188-5191, 2001.

M. Rossi, M. Huber, D. Bruß, and C. Macchiavello, Quantum hypergraph states, New Journal of Physics, vol.15, issue.11, p.113022, 2013.

D. Schlingemann and R. F. Werner, Quantum error-correcting codes associated with graphs, Physical Review A, vol.65, 2001.

C. Schröder-de-witt and V. Zamdzhiev, The ZX-calculus is incomplete for quantum mechanics, QPL 2014, Electronic Proceedings in Theoretical Computer Science, pp.285-292, 2014.

P. Selinger, Dagger compact closed categories and completely positive maps, Electronic Notes in Theoretical Computer Science, vol.170, pp.139-163, 2007.

P. Selinger, Generators and relations for n-qubit Clifford operators, Logical Methods in Computer Science, vol.11, issue.2, 2015.

P. Selinger and X. Bian, Relations for Clifford+T operators on two qubits, 2015.

A. Shamir, How to share a secret, Communications of the ACM, vol.22, issue.11, pp.612-613, 1979.

J. A. Telle, Complexity of domination-type problems in graphs, Nordic Journal of Computing, vol.1, pp.157-171, 1994.

M. Van-den-nest, A. Miyake, W. Dür, and H. J. Briegel, Universal resources for measurement-based quantum computation, Phys. Rev. Lett, vol.97, p.150504, 2006.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter et al., Experimental one-way quantum computing, Nature, vol.434, issue.7030, pp.169-176, 2005.

W. K. Wootters and W. H. Zurek, A single quantum cannot be cloned, Nature, vol.299, pp.802-803, 1982.

A. Yao, Quantum circuit complexity, Proc. 34th IEEE Symposium on Foundation of Computer Science, p.75, 1993.