## Planat, Michel

Compute Distance To:
 Author ID: planat.michel Published as: Planat, Michel; Planat, M. External Links: ORCID
 Documents Indexed: 60 Publications since 1980 2 Contributions as Editor Reviewing Activity: 6 Reviews Co-Authors: 29 Co-Authors with 45 Joint Publications 601 Co-Co-Authors
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### Co-Authors

 15 single-authored 24 Saniga, Metod 7 Pracna, Petr 7 Solé, Patrick 4 Holweck, Frédéric 4 Rosu, Haret C. 3 Havlicek, Hans 3 Kibler, Maurice R. 3 Lévay, Péter 2 Baboin, Anne-Céline 1 Amaral, Marcelo M. 1 Anselmi, Fabio 1 Aschheim, Raymond 1 François, Edouard 1 Friedt, J.-M. 1 Gillet, Denis 1 Giorgetti, Alain 1 Irwin, Klee 1 Jorrand, Philippe 1 Kurizki, Gershon 1 Laude, Vincent 1 Luque, Jean-Gabriel 1 Minarovjech, M. 1 Omar, Sami 1 Perrine, Serge 1 Schleich, Wolfgang P. 1 Theobald, Genevieve 1 Ul Haq, Rukhsan 1 Vourdas, Apostol 1 Zainuddin, Hishamuddin
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### Serials

 7 Journal of Physics A: Mathematical and Theoretical 4 International Journal of Modern Physics B 4 Theoretical and Mathematical Physics 4 Chaos, Solitons and Fractals 4 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 2 International Journal of Theoretical Physics 2 Physics Letters. A 2 Quantum Information Processing 2 International Journal of Geometric Methods in Modern Physics 2 Quantum Information & Computation 2 Mathematics 1 Modern Physics Letters A 1 Acustica 1 Letters in Mathematical Physics 1 Physica A 1 Reports on Mathematical Physics 1 Journal of Physics A: Mathematical and General 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Journal de Théorie des Nombres de Bordeaux 1 Fractals 1 Notes on Number Theory and Discrete Mathematics 1 Integers 1 Foundations of Physics 1 Revue du CETHEDEC 1 Lecture Notes in Physics 1 Revista Mexicana Física 1 Advanced Studies in Theoretical Physics 1 Journal of Combinatorics and Number Theory 1 Advances in Mathematical Physics 1 Symmetry 1 General Mathematics Notes 1 Journal of Discrete Mathematics 1 Annales de l’Institut Henri Poincaré D. Combinatorics, Physics and their Interactions (AIHPD) 1 Quantum Studies: Mathematics and Foundations
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### Fields

 45 Quantum theory (81-XX) 19 Number theory (11-XX) 17 Geometry (51-XX) 10 Group theory and generalizations (20-XX) 8 Algebraic geometry (14-XX) 7 Statistical mechanics, structure of matter (82-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Information and communication theory, circuits (94-XX) 4 Dynamical systems and ergodic theory (37-XX) 2 General and overarching topics; collections (00-XX) 2 Field theory and polynomials (12-XX) 2 Topological groups, Lie groups (22-XX) 2 Functional analysis (46-XX) 2 Manifolds and cell complexes (57-XX) 2 Mechanics of particles and systems (70-XX) 2 Mechanics of deformable solids (74-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Commutative algebra (13-XX) 1 Nonassociative rings and algebras (17-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Relativity and gravitational theory (83-XX)

### Citations contained in zbMATH Open

45 Publications have been cited 155 times in 84 Documents Cited by Year
A survey of finite algebraic geometrical structures underlying mutually unbiased quantum measurements. Zbl 1106.81023
Planat, Michel; Rosu, Haret C.; Perrine, Serge
2006
Hjelmslev geometry of mutually unbiased bases. Zbl 1086.51004
Saniga, Metod; Planat, Michel
2006
Viewing sets of mutually unbiased bases as arcs in finite projective planes. Zbl 1072.51009
Saniga, Metod; Planat, Michel
2005
A $$\text{SU}(2)$$ recipe for mutually unbiased bases. Zbl 1093.81035
Kibler, Maurice R.; Planat, Michel
2006
Projective line over the finite quotient ring $$\mathrm{GF}(2)[x]/\langle x^{3}-x\rangle$$ and quantum entanglement: the Mermin “magic” square/pentagram. Zbl 1139.81330
Saniga, M.; Planat, M.; Minarovjech, M.
2007
On the Pauli graphs on $$N$$-qudits. Zbl 1154.81324
Planat, Michel; Saniga, Metod
2008
Multiple qubits as symplectic polar spaces of order two. Zbl 1122.81026
Saniga, Metod; Planat, Michel
2007
Geometry of contextuality from Grothendieck’s coset space. Zbl 1327.81265
Planat, Michel
2015
Quantum contextual finite geometries from dessins d’enfants. Zbl 1327.11042
Planat, Michel; Giorgetti, Alain; Holweck, Frédéric; Saniga, Metod
2015
Three-qubit entangled embeddings of $$CPT$$ and Dirac groups within $$E_8$$ Weyl group. Zbl 1190.81029
Planat, Michel
2010
Projective line over the finite quotient ring $$\text{GF}(2)[x]/\langle x^{3} - x\rangle$$ and quantum entanglement: theoretical background. Zbl 1119.81016
Saniga, M.; Planat, M.
2007
Twin “Fano-snowflakes” over the smallest ring of ternions. Zbl 1140.51300
Saniga, Metod; Havlicek, Hans; Planat, Michel; Pracna, Petr
2008
Projective ring line encompassing two-qubits. Zbl 1145.81344
Saniga, M.; Planat, M.; Pracna, P.
2008
Quantum entanglement and projective ring geometry. Zbl 1134.81319
Planat, Michel; Saniga, Metod; Kibler, Maurice R.
2006
Pauli graphs when the Hilbert space dimension contains a square: why the Dedekind psi function? Zbl 1206.81029
Planat, Michel
2011
Distinguished three-qubit ‘magicity’ via automorphisms of the split Cayley hexagon. Zbl 1270.81048
Planat, Michel; Saniga, Metod; Holweck, Frédéric
2013
Cyclotomy and Ramanujan sums in quantum phase locking. Zbl 1098.81748
Planat, Michel; Rosu, Haret C.
2003
The Veldkamp space of two-qubits. Zbl 1138.51003
Saniga, Metod; Planat, Michel; Pracna, Petr; Havlicek, Hans
2007
A classification of the projective lines over small rings. Zbl 1134.51301
Saniga, Metod; Planat, Michel; Kibler, Maurice R.; Pracna, Petr
2007
Veldkamp-space aspects of a sequence of nested binary Segre varieties. Zbl 1326.51004
Saniga, Metod; Havlicek, Hans; Holweck, Frédéric; Planat, Michel; Pracna, Petr
2015
The Robin inequality for 7-free integers. Zbl 1266.11106
Solé, Patrick; Planat, Michel
2012
Finite geometries in quantum theory: from Galois (fields) to Hjelmslev (rings). Zbl 1093.81045
Saniga, Metod; Planat, Michel
2006
Group theory for quantum gates and quantum coherence. Zbl 1139.81022
Planat, Michel; Jorrand, Philippe
2008
Multi-line geometry of qubit-qutrit and higher-order Pauli operators. Zbl 1140.81338
Planat, Michel; Baboin, Anne-Céline; Saniga, Metod
2008
Riemann hypothesis and quantum mechanics. Zbl 1215.82005
Planat, Michel; Solé, Patrick; Omar, Sami
2011
Singularity of type $$D_4$$ arising from four-qubit systems. Zbl 1287.81035
Holweck, Frédéric; Luque, Jean-Gabriel; Planat, Michel
2014
The magic of universal quantum computing with permutations. Zbl 1400.81072
Planat, Michel; Ul Haq, Rukhsan
2017
Extreme values of the Dedekind $$\Psi$$ function. Zbl 1266.11107
Solé, Patrick; Planat, Michel
2011
Geometric hyperplanes of the near hexagon $$L_{3} \times GQ(2, 2)$$. Zbl 1185.51008
Saniga, Metod; Lévay, Péter; Planat, Michel; Pracna, Petr
2010
‘Magic’ configurations of three-qubit observables and geometric hyperplanes of the smallest split Cayley hexagon. Zbl 1271.51004
Saniga, Metod; Planat, Michel; Pracna, Petr; Lévay, Péter
2012
On the geometry and invariants of qubits, quartits and octits. Zbl 1216.81051
Planat, M.
2011
A moonshine dialogue in mathematical physics. Zbl 1328.01071
Planat, Michel
2015
Improving Riemann prime counting. Zbl 1351.11058
Planat, Michel; Solé, Patrick
2015
From Planck to Ramanujan: a quantum $$1/f$$ noise in equilibrium. Zbl 1256.82003
Planat, Michel
2002
Clifford groups of quantum gates, BN-pairs and smooth cubic surfaces. Zbl 1156.81352
Planat, Michel; Solé, Patrick
2009
$$1/f$$ frequency noise in a communication receiver and the Riemann hypothesis. Zbl 1112.94300
Planat, Michel
2000
Geometric contextuality from the Maclachlan-Martin Kleinian groups. Zbl 1338.81026
Planat, Michel
2016
Universal quantum computing and three-manifolds. Zbl 1425.81021
Planat, Michel; Aschheim, Raymond; Amaral, Marcelo M.; Irwin, Klee
2018
Thermal $$1/f$$ noise from the theory of partitions: application to a quartz resonator. Zbl 1010.82018
Planat, Michel
2003
Huyghens, Bohr, Riemann and Galois: phase-locking. Zbl 1093.81042
Planat, Michel
2006
On the fine structure of the projective line over $$\text{GF(2)}\otimes\text{GF(2)}\otimes\text{GF(2)}$$. Zbl 1138.51300
Saniga, Metod; Planat, Michel
2008
A sequence of qubit-qudit Pauli groups as a nested structure of doilies. Zbl 1220.81044
Saniga, Metod; Planat, Michel
2011
Clifford group dipoles and the enactment of Weyl/Coxeter group $$W(E_8)$$ by entangling gates. Zbl 1225.81038
Planat, Michel
2011
Qudits of composite dimension, mutually unbiased bases and projective ring geometry. Zbl 1128.81006
Planat, Michel; Baboin, Anne-Céline
2007
Projective planes over “Galois” double numbers and a geometrical principle of complementarity. Zbl 1151.51300
Saniga, Metod; Planat, Michel
2008
Universal quantum computing and three-manifolds. Zbl 1425.81021
Planat, Michel; Aschheim, Raymond; Amaral, Marcelo M.; Irwin, Klee
2018
The magic of universal quantum computing with permutations. Zbl 1400.81072
Planat, Michel; Ul Haq, Rukhsan
2017
Geometric contextuality from the Maclachlan-Martin Kleinian groups. Zbl 1338.81026
Planat, Michel
2016
Geometry of contextuality from Grothendieck’s coset space. Zbl 1327.81265
Planat, Michel
2015
Quantum contextual finite geometries from dessins d’enfants. Zbl 1327.11042
Planat, Michel; Giorgetti, Alain; Holweck, Frédéric; Saniga, Metod
2015
Veldkamp-space aspects of a sequence of nested binary Segre varieties. Zbl 1326.51004
Saniga, Metod; Havlicek, Hans; Holweck, Frédéric; Planat, Michel; Pracna, Petr
2015
A moonshine dialogue in mathematical physics. Zbl 1328.01071
Planat, Michel
2015
Improving Riemann prime counting. Zbl 1351.11058
Planat, Michel; Solé, Patrick
2015
Singularity of type $$D_4$$ arising from four-qubit systems. Zbl 1287.81035
Holweck, Frédéric; Luque, Jean-Gabriel; Planat, Michel
2014
Distinguished three-qubit ‘magicity’ via automorphisms of the split Cayley hexagon. Zbl 1270.81048
Planat, Michel; Saniga, Metod; Holweck, Frédéric
2013
The Robin inequality for 7-free integers. Zbl 1266.11106
Solé, Patrick; Planat, Michel
2012
‘Magic’ configurations of three-qubit observables and geometric hyperplanes of the smallest split Cayley hexagon. Zbl 1271.51004
Saniga, Metod; Planat, Michel; Pracna, Petr; Lévay, Péter
2012
Pauli graphs when the Hilbert space dimension contains a square: why the Dedekind psi function? Zbl 1206.81029
Planat, Michel
2011
Riemann hypothesis and quantum mechanics. Zbl 1215.82005
Planat, Michel; Solé, Patrick; Omar, Sami
2011
Extreme values of the Dedekind $$\Psi$$ function. Zbl 1266.11107
Solé, Patrick; Planat, Michel
2011
On the geometry and invariants of qubits, quartits and octits. Zbl 1216.81051
Planat, M.
2011
A sequence of qubit-qudit Pauli groups as a nested structure of doilies. Zbl 1220.81044
Saniga, Metod; Planat, Michel
2011
Clifford group dipoles and the enactment of Weyl/Coxeter group $$W(E_8)$$ by entangling gates. Zbl 1225.81038
Planat, Michel
2011
Three-qubit entangled embeddings of $$CPT$$ and Dirac groups within $$E_8$$ Weyl group. Zbl 1190.81029
Planat, Michel
2010
Geometric hyperplanes of the near hexagon $$L_{3} \times GQ(2, 2)$$. Zbl 1185.51008
Saniga, Metod; Lévay, Péter; Planat, Michel; Pracna, Petr
2010
Clifford groups of quantum gates, BN-pairs and smooth cubic surfaces. Zbl 1156.81352
Planat, Michel; Solé, Patrick
2009
On the Pauli graphs on $$N$$-qudits. Zbl 1154.81324
Planat, Michel; Saniga, Metod
2008
Twin “Fano-snowflakes” over the smallest ring of ternions. Zbl 1140.51300
Saniga, Metod; Havlicek, Hans; Planat, Michel; Pracna, Petr
2008
Projective ring line encompassing two-qubits. Zbl 1145.81344
Saniga, M.; Planat, M.; Pracna, P.
2008
Group theory for quantum gates and quantum coherence. Zbl 1139.81022
Planat, Michel; Jorrand, Philippe
2008
Multi-line geometry of qubit-qutrit and higher-order Pauli operators. Zbl 1140.81338
Planat, Michel; Baboin, Anne-Céline; Saniga, Metod
2008
On the fine structure of the projective line over $$\text{GF(2)}\otimes\text{GF(2)}\otimes\text{GF(2)}$$. Zbl 1138.51300
Saniga, Metod; Planat, Michel
2008
Projective planes over “Galois” double numbers and a geometrical principle of complementarity. Zbl 1151.51300
Saniga, Metod; Planat, Michel
2008
Projective line over the finite quotient ring $$\mathrm{GF}(2)[x]/\langle x^{3}-x\rangle$$ and quantum entanglement: the Mermin “magic” square/pentagram. Zbl 1139.81330
Saniga, M.; Planat, M.; Minarovjech, M.
2007
Multiple qubits as symplectic polar spaces of order two. Zbl 1122.81026
Saniga, Metod; Planat, Michel
2007
Projective line over the finite quotient ring $$\text{GF}(2)[x]/\langle x^{3} - x\rangle$$ and quantum entanglement: theoretical background. Zbl 1119.81016
Saniga, M.; Planat, M.
2007
The Veldkamp space of two-qubits. Zbl 1138.51003
Saniga, Metod; Planat, Michel; Pracna, Petr; Havlicek, Hans
2007
A classification of the projective lines over small rings. Zbl 1134.51301
Saniga, Metod; Planat, Michel; Kibler, Maurice R.; Pracna, Petr
2007
Qudits of composite dimension, mutually unbiased bases and projective ring geometry. Zbl 1128.81006
Planat, Michel; Baboin, Anne-Céline
2007
A survey of finite algebraic geometrical structures underlying mutually unbiased quantum measurements. Zbl 1106.81023
Planat, Michel; Rosu, Haret C.; Perrine, Serge
2006
Hjelmslev geometry of mutually unbiased bases. Zbl 1086.51004
Saniga, Metod; Planat, Michel
2006
A $$\text{SU}(2)$$ recipe for mutually unbiased bases. Zbl 1093.81035
Kibler, Maurice R.; Planat, Michel
2006
Quantum entanglement and projective ring geometry. Zbl 1134.81319
Planat, Michel; Saniga, Metod; Kibler, Maurice R.
2006
Finite geometries in quantum theory: from Galois (fields) to Hjelmslev (rings). Zbl 1093.81045
Saniga, Metod; Planat, Michel
2006
Huyghens, Bohr, Riemann and Galois: phase-locking. Zbl 1093.81042
Planat, Michel
2006
Viewing sets of mutually unbiased bases as arcs in finite projective planes. Zbl 1072.51009
Saniga, Metod; Planat, Michel
2005
Cyclotomy and Ramanujan sums in quantum phase locking. Zbl 1098.81748
Planat, Michel; Rosu, Haret C.
2003
Thermal $$1/f$$ noise from the theory of partitions: application to a quartz resonator. Zbl 1010.82018
Planat, Michel
2003
From Planck to Ramanujan: a quantum $$1/f$$ noise in equilibrium. Zbl 1256.82003
Planat, Michel
2002
$$1/f$$ frequency noise in a communication receiver and the Riemann hypothesis. Zbl 1112.94300
Planat, Michel
2000
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### Cited by 108 Authors

 23 Planat, Michel 18 Saniga, Metod 6 Holweck, Frédéric 5 Kibler, Maurice R. 5 Pracna, Petr 4 Havlicek, Hans 3 Bartnicka, Edyta 3 Lévay, Péter 3 Revzen, Michael 2 Giorgetti, Alain 2 Roy, Aidan 1 Alfi, Alireza 1 Amaral, Marcelo M. 1 An, Hao 1 Anselmi, Fabio 1 Aoudjit, Safia 1 Aschheim, Raymond 1 Axler, Christian 1 Baboin, Anne-Céline 1 Belhaj, Adil 1 Bengtsson, Ingemar 1 Bensed, M. 1 Benslimane, Zakariae 1 Berkane, Djamel 1 Boulmier, Jérôme 1 Brierley, Stephen D. 1 Bruinier, Jan Hendrik 1 Cao, Haitao 1 Cao, Xiwang 1 Cassam-Chenaï, Patrick 1 Chapman, Adrian 1 Choi, Seongsoo 1 Chou, Wunseng 1 Chung, Jinwook 1 Cresson, Jacky 1 Crompton, Peter R. 1 De Baerdemacker, Stijn 1 De Vos, Alexis 1 Dhont, Guillaume 1 Dubois, Catherine 1 Durt, Thomas 1 Dusart, Pierre 1 Elman, Samuel J. 1 Englert, Berthold-Georg 1 Fan, Jinping 1 Fickus, Matthew C. 1 Flammia, Steven T. 1 Fowler, Christopher F. 1 Garcia, Stephan Ramon 1 Green, Richard M. 1 Hall, Joanne L. 1 Howe, Roger Evans 1 Hughes, Barry D. 1 Irwin, Klee 1 Jaffali, Hamza 1 Kalev, Amir 1 Karaali, Gizem 1 Keppens, Dirk 1 Khanna, Faqir C. 1 Kosiorek, Jarosław 1 Krenkel, T. E. 1 Leung, Debbie W. 1 Luque, Jean-Gabriel 1 Mahecha, Jorge 1 Mančinska, Laura 1 Man’ko, Margarita A. 1 Man’ko, Vladimir Ivanovich 1 Mann, Ady 1 Matraś, Andrzej 1 Matthews, William 1 Minarovjech, M. 1 Mixon, Dustin G. 1 Mohammadi, Leila 1 Morrill, Thomas 1 Ninham, Barry W. 1 Nounouh, Ismaël 1 Odehnal, Boris 1 Ono, Ken 1 Ouyang, Yingkai 1 Ozols, Maris A. 1 Pankov, Mark 1 Patras, Frédéric 1 Perrine, Serge 1 Pinard, Maxime 1 Platt, David John 1 Rao, Asha 1 Rosu, Haret C. 1 Saouter, Yannick 1 Sarkar, Rahul 1 Scott, Andrew James 1 Sedra, Moulay Brahim 1 Segui, Antonio 1 Solé, Patrick 1 Sümmermann, Moritz L. 1 Sutherland, Andrew V. 1 Szöllősi, Ferenc 1 Thibon, Jean-Yves 1 Ul Haq, Rukhsan 1 van den Berg, Ewout 1 Walsh, Timothy R. S. ...and 8 more Authors
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### Cited in 45 Serials

 6 Journal of Mathematical Physics 6 International Journal of Geometric Methods in Modern Physics 5 Theoretical and Mathematical Physics 4 Linear Algebra and its Applications 3 International Journal of Modern Physics B 3 International Journal of Theoretical Physics 3 Chaos, Solitons and Fractals 3 Results in Mathematics 3 Quantum Information Processing 3 Mathematics 3 Quantum Studies: Mathematics and Foundations 2 Bulletin of the Australian Mathematical Society 2 Communications in Mathematical Physics 2 Proceedings of the American Mathematical Society 2 Journal of Mathematical Sciences (New York) 2 The Ramanujan Journal 2 Nonlinear Dynamics 2 Physical Review A, Third Series 1 Letters in Mathematical Physics 1 Physica A 1 Reports on Mathematical Physics 1 Mathematics of Computation 1 The Mathematical Intelligencer 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Journal of Number Theory 1 Kybernetika 1 Acta Mathematicae Applicatae Sinica. English Series 1 Formal Aspects of Computing 1 Aequationes Mathematicae 1 Indagationes Mathematicae. New Series 1 Journal de Théorie des Nombres de Bordeaux 1 The Journal of Fourier Analysis and Applications 1 Journal of Mathematical Chemistry 1 Journal of Integer Sequences 1 Integers 1 Entropy 1 International Journal of Quantum Information 1 Foundations of Physics 1 Journal of Physics A: Mathematical and Theoretical 1 Ars Mathematica Contemporanea 1 Advances in Mathematical Physics 1 Symmetry 1 Axioms 1 Annales de l’Institut Henri Poincaré D. Combinatorics, Physics and their Interactions (AIHPD) 1 Research in the Mathematical Sciences
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### Cited in 29 Fields

 51 Quantum theory (81-XX) 21 Geometry (51-XX) 20 Number theory (11-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 11 Group theory and generalizations (20-XX) 10 Algebraic geometry (14-XX) 7 Combinatorics (05-XX) 5 Field theory and polynomials (12-XX) 5 Associative rings and algebras (16-XX) 4 Topological groups, Lie groups (22-XX) 4 Computer science (68-XX) 4 Statistical mechanics, structure of matter (82-XX) 4 Information and communication theory, circuits (94-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Operator theory (47-XX) 3 Manifolds and cell complexes (57-XX) 2 Commutative algebra (13-XX) 2 Nonassociative rings and algebras (17-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Numerical analysis (65-XX) 2 Relativity and gravitational theory (83-XX) 2 Systems theory; control (93-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Abstract harmonic analysis (43-XX) 1 Functional analysis (46-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Operations research, mathematical programming (90-XX)