Research

Research

Interests [WordCloud]

  • Random matrices and tensors
  • Free probability theory
  • Quantum information theory

Editorial work

AIHPD Journal I am an editor for Annales de l’Institut Henri Poincaré D, a journal specializing in combinatorics, physics and their interactions. The journal is dedicated to publishing high-quality original research articles and survey articles in which combinatorics and physics interact in both directions. Combinatorial papers should be motivated by potential applications to physical phenomena or models, while physics papers should contain some interesting combinatorial development.

Quantum Journal I am an editor for Quantum, a non-profit and open access peer-reviewed journal that provides high visibility for quality research on quantum science and related fields.

AOT Journal I am an editor for Advances in Operator Theory, a journal that disseminates research papers featuring original findings, deep ideas, novel proofs, and profound influence in contemporary mathematical analysis, with a particular emphasis on operator theory and functional analysis.

IDAQP Journal I am an editor for Infinite Dimensional Analysis, Quantum Probability and Related Topics, which is a highly interdisciplinary journal, devoted to papers in infinite dimensional analysis and quantum probability with connections to classical probability, stochastic analysis, mathematical physics.

Funding

  • PHC Star – Applications of random matrix theory and abstract harmonic analysis to quantum information theory – PI France, 2022-2024
  • ANR ESQuisses – Évolutions Stochastiques Quantiques – PI, 2021-2025
  • ANR STARS – member, 2021-2025

Papers

Recent preprints

  1. Towards unconditional uncloneable encryption (with Pierre Botteron, Anne Broadbent, Eric Culf, Clément Pellegrini, Denis Rochette) [arXiv]
  2. A Max-Flow approach to Random Tensor Networks (with Khurshed Fitter, Faedi Loulidi) [arXiv]
  3. On random classical marginal problems with applications to quantum information theory (with Ankit Kumar Jha) [arXiv]
  4. Random covariant quantum channels (with Sang-Jun Park) [arXiv]
  5. On the simulation of quantum multimeters (with Leevi Leppäjärvi and Andreas Bluhm) [arXiv]
  6. Monogamy of highly symmetric states (with Rene Allerstorfer, Matthias Christandl, Dmitry Grinko, Maris Ozols, Denis Rochette, and Philip Verduyn Lunel) [arXiv]
  7. The Sk-circular limit of random tensor flattenings (with Stéphane Dartois and Camille Male) [arXiv]
  8. A physical noise model for quantum measurements (with Faedi Loulidi and Clément Pellegrini) [arXiv]
  9. Estimating the entanglement of random multipartite quantum states (with Khurshed Fitter and Cécilia Lancien) [arXiv]

  10. Ergodic theory of diagonal orthogonal covariant quantum channels (with Satvik Singh and Nilanjana Datta) [arXiv]

  11. On the spectral gap of random quantum channels (with Carlos E. González-Guillén and Marius Junge) [arXiv]
  12. de Finetti reductions for partially exchangeable probability distributions (with Ivan Bardet and Cécilia Lancien) [arXiv]

Published/accepted papers

  1. Generating random Gaussian states (with Leevi Leppäjärvi and Ritabrata Sengupta) - J. Math. Phys. 65, 082201 (2024) [journal] [arXiv]
  2. Generating series and matrix models for meandric systems with one shallow side (with Motohisa Fukuda) - Ann. Inst. Henri Poincaré Comb. Phys. Interact. 11 (2024), no. 2, pp. 299–330 [journal] [arXiv]
  3. Algebra of Nonlocal Boxes and the Collapse of Communication Complexity (with Pierre Botteron, Anne Broadbent, Reda Chhaibi, Clément Pellegrini) - Quantum 8, 1402 (2024) [journal] [arXiv]
  4. Generalized unistochastic matrices (with Zikun Ouyang and Anna Szczepanek) - to appear in Lin. Alg. Appl. [journal] [arXiv]
  5. Polytope compatibility – from quantum measurements to magic squares (with Andreas Bluhm and Simon Schmidt) – J. Math. Phys. 64, 122201 (2023) [journal] [arXiv]
  6. The Asymmetric Quantum Cloning Region (with Clément Pellegrini and Denis Rochette) – Letters in Mathematical Physics 113, 74 (2023) [journal] [arXiv]
  7. Measurement incompatibility vs. Bell non-locality: an approach via tensor norms (with Faedi Loulidi) – PRX Quantum 3, 040325 (2022) [journal] [arXiv]
  8. Order preserving maps on quantum measurements (with Teiko Heinosaari and Maria Jivulescu) – Quantum 6, 853 (2022) [journal] [arXiv]
  9. Entanglement criteria for the bosonic and fermionic induced ensembles (with Stephane Dartois and Adrian Tanasa) – Quantum Information Processing 21, 376 (2022) [journal] [arXiv]
  10. The PPT² conjecture holds for all Choi-type maps (with Satvik Singh) – Annales Henri Poincaré 23, pages 3311–3329 (2022) [journal] [arXiv]
  11. Incompatibility in general probabilistic theories, generalized spectrahedra, and tensor norms (with Andreas Bluhm and Anna Jenčová) – Comm. Math. Phys. 393(3), 1125-1198 (2022) [journal] arXiv]
  12. A Fisher information-based incompatibility criterion for quantum channels (with Qing-Hua Zhang) – Entropy, 24(6), 805 (2022) [journal] [arXiv]
  13. A tensor norm approach to quantum compatibility (with Andreas Bluhm) – J. Math. Phys. 63, 062201 (2022) [journal] [arXiv]
  14. Diagonal unitary and orthogonal symmetries in quantum theory II: Evolution operators (with Satvik Singh) – J. Phys. A: Math. Theor. 55 255302 (2022) [journal] [arXiv]
  15. Multipartite entanglement detection via projective tensor norms (with Maria Jivulescu and Cécilia Lancien) – Ann. Henri Poincaré (2022) [journal] [arXiv]
  16. Maximal violation of steering inequalities and the matrix cube (with Andreas Bluhm) – Quantum 6, 656 (2022) [journal] [arXiv]
  17. A geometrical description of the universal 1→2 asymmetric quantum cloning region (with Clément Pellegrini and Denis Rochette) – Quantum Information Processing volume 20, 333 (2021) [journal] [arXiv]
  18. A refinement of Reznick’s Positivstellensatz with applications to quantum information theory (with Alexander Müller-Hermes and David Reeb) – Quantum 7, 1001 (2023) [journal] [arXiv]
  19. Diagonal unitary and orthogonal symmetries in quantum theory (with Satvik Singh) – Quantum 5, 519 (2021) [journal] [arXiv]
  20. Generating random quantum channels (with Ryszard Kukulski, Łukasz Pawela, Zbigniew Puchała, and Karol Życzkowski) – Journal of Mathematical Physics 62, 062201 (2021) [journal] [arXiv]
  21. SudoQ – a quantum variant of the popular game (with Jordi Pillet) – Quantum Information & Computation Vol. 21 No. 9&10 (2021) [journal] [arXiv]
  22. The compatibility dimension of quantum measurements (with Faedi Loulidi) – Journal of Mathematical Physics 62, 042205 (2021) [journal] [arXiv]
  23. Sinkhorn algorithm for quantum permutation groups (with Simon Schmidt and Moritz Weber) – Experimental Mathematics [journal] [arXiv]
  24. A graphical calculus for integration over random diagonal unitary matrices (with Satvik Singh) – Linear Algebra and its Applications 613, 46-86 (2021) [journal] [arXiv]
  25. Random positive operator valued measures (with Teiko Heinosaari and Maria Jivulescu) – Journal of Mathematical Physics 61, 042202 (2020) [journal] [arXiv]
  26. Compatibility of quantum measurements and inclusion constants for the matrix jewel (with Andreas Bluhm) – SIAM J. Appl. Algebra Geometry, 4(2), 255–296 (2020) [journal] [arXiv]
  27. RTNI – A symbolic integrator for Haar-random tensor networks (with Motohisa Fukuda and Robert König) – J. Phys. A: Math. Theor. 52 425303 (2019) [journal] [arXiv] [code] [a light, online version of the main integration routine]
  28. On the joint distribution of the marginals of multipartite random quantum states (with Stephane Dartois and Luca Lionni) – Random Matrices: Theory and Applications Vol. 09, No. 03, 2050010 (2020) [journal] [arXiv]
  29. Joint measurability of quantum effects and the matrix diamond (with Andreas Bluhm) – Journal of Mathematical Physics 59, 112202 (2018) [journal] [arXiv]
  30. Operator Schmidt ranks of bipartite unitary matrices (with Alexander Müller-Hermes) – Lin. Alg. and its Appl. 557, 174-187 (2018) [journal] [arXiv]
  31. On the separability of unitarily invariant random quantum states – the unbalanced regime – Adv. Math. Phys., vol. 2018, Article ID 7105074 (2018) [journal] [arXiv]
  32. Almost all quantum channels are equidistant (with Zbigniew Puchała, Łukasz Pawela, Karol Życzkowski) – Journal of Mathematical Physics 59, 052201 (2018) [journal] [arXiv]
  33. On the minimum output entropy of random orthogonal quantum channels (with Motohisa Fukuda) – IEEE Trans. Inf. Th. 64, no. 2, 1374 – 1384 (2018) [journal] [arXiv]
  34. Enumerating meandric systems with large number of components (with Motohisa Fukuda) – Ann. Inst. Henri Poincaré D, 6, 4, 607-640 (2019) [journal] [arXiv]
  35. Almost Hadamard matrices with complex entries (with Teodor Banica) – Adv. Oper. Theory 3, no. 1, 149–189 (2018) [journal] [arXiv]
  36. On symmetric decompositions of positive operators (with Maria Jivulescu and Pasc Gavruta) – J. Phys. A: Math. Theor. 50 165303 (2017) [journal] [arXiv]
  37. On bipartite unitary matrices generating subalgebra-preserving quantum operations (with Tristan Benoist) – Linear Algebra and its Applications 521, 70–103 (2017) – [journal] [arXiv]
  38. Flat matrix models for quantum permutation groups (with Teodor Banica) – Adv. Appl. Math. 83, 24-46 (2017) [journal] [arXiv]
  39. On some classes of bipartite unitary operators (with Julien Deschamps and Clément Pellegrini) – J. Phys. A: Math. Theor. 49 335301 (2016) [journal] [arXiv]
  40. Random and free positive maps with applications to entanglement detection (with Benoit Collins and Patrick Hayden) – International Mathematics Research Notices, rnw054 (2016) [journal] [arXiv]
  41. On the asymptotic distribution of block-modified random matrices (with Octavio Arizmendi and Carlos Vargas) – Journal of Mathematical Physics 57, 015216 (2016) [journal] [arXiv]
  42. Random matrix techniques in quantum information theory (with Benoit Collins) – Journal of Mathematical Physics 57, 015215 (2016) [journal] [arXiv]
  43. Almost one bit violation for the additivity of the minimum output entropy (with Serban Belinschi and Benoit Collins) – Comm. Math. Phys. 341(3), 885-909 (2016) [journal] [arXiv]
  44. Thresholds for reduction-related entanglement criteria in quantum information theory (with Maria Anastasia Jivulescu and Nicolae Lupa) – Quantum Information and Computation, Vol. 15, No. 13-14 (2015) 1165–1184 [journal] [arXiv]
  45. Additivity rates and PPT property for random quantum channels (with Motohisa Fukuda) – Ann. Math. Blaise Pascal 22, 1-72 (2015) [journal] [arXiv]
  46. On the convergence of output sets of quantum channels (with Benoit Collins and Motohisa Fukuda) – J. Operator Theory, 73:2(2015), 333–360 [journal] [arXiv]
  47. Quantum channels with polytopic images and image additivity (with Motohisa Fukuda, and Michael M. Wolf) – IEEE Transactions on Information Theory, vol.61, no.4, pp. 1851-1859 (2015) [journal] [arXiv]
  48. Positive reduction from spectra (with Maria Anastasia Jivulescu, Nicolae Lupa, and David Reeb) – Linear Algebra and its Applications 469 (2015) 276–304 [journal] [arXiv]
  49. On the reduction criterion for random quantum states (with Maria Anastasia Jivulescu and Nicolae Lupa) – J. Math. Phys. 55, 112203 (2014) [journal] [arXiv]
  50. Analytic aspects of the circulant Hadamard conjecture (with Teodor Banica and Jean-Marc Schlenker) – Ann. Math. Blaise Pascal 21 (2014), 25-59 [journal] [arXiv]
  51. Asymptotically well-behaved input states do not violate additivity for conjugate pairs of random quantum channels (with Motohisa Fukuda) – Comm. Math. Phys. Vol. 328, No. 3 (2014), 995-1021 [journal] [arXiv]
  52. A universal set of qubit quantum channels (with Daniel Braun, Olivier Giraud, Clement Pellegrini and Marko Znidaric) – J. Phys. A: Math. Theor. 47 (2014) 135302 [journal] [arXiv]
  53. Submatrices of Hadamard matrices: complementation results (with Teodor Banica and Jean-Marc Schlenker) – Electron. J. Linear Algebra 27 (2014), 197-212 [journal] [arXiv]
  54. Area law for random graph states (with Benoît Collins and Karol Zyczkowski) – J. Phys. A: Math. Theor. 46 305302 (2013) [journal] [arXiv]
  55. Almost Hadamard matrices: the case of arbitrary exponents (with Teodor Banica) – Discrete Applied Mathematics, vol. 161, no. 16–17, 2367-2379 (2013) [journal] [arXiv]
  56. Random pure quantum states via unitary Brownian motion (with Clément Pellegrini) – Electron. Commun. Probab. 18 (2013), no. 27, 1–13 [journal] [arXiv]
  57. Low entropy output states for products of random unitary channels (with Benoit Collins and Motohisa Fukuda) – Random Matrices: Theory Appl. 02, 1250018 (2013) [journal] [arXiv]
  58. Almost Hadamard matrices: general theory and examples (with Teodor Banica and Karol Zyczkowski) – Open Systems & Information Dynamics, Vol. 19, No. 4, 1250024 (2012) [journal] [arXiv]
  59. Realigning random states (with Guillaume Aubrun) – J. Math. Phys. 53, 102210 (2012) [journal] [arXiv]
  60. Block-modified Wishart matrices and free Poisson laws (with Teodor Banica) – Houston Journal of Mathematics, Volume 41, No. 1 (2015) [journal] [arXiv]
  61. The absolute positive partial transpose property for random induced states (with Benoît Collins and Deping Ye) – Random Matrices: Theory Appl. 01, 1250002 (2012) [journal] [arXiv]
  62. Towards a state minimizing the output entropy of a tensor product of random quantum channels (with Benoît Collins and Motohisa Fukuda) – J. Math. Phys. 53, 032203 (2012) [journal] [arXiv]
  63. The multiplicative property characterizes $\ell_p$ and $L_p$ norms (with Guillaume Aubrun) – Confluentes Mathematici, Volume 3, Number 4 (2011), pp. 637-647 [journal] [arXiv]
  64. Asymptotic eigenvalue distributions of block-transposed Wishart matrices (with Teodor Banica) – J. Theoret. Probab. 26 (2013), 855-869 [journal] [arXiv]
  65. Eigenvectors and eigenvalues in a random subspace of a tensor product (with Serban Belinschi and Benoît Collins) – Inventiones mathematicae, vol. 190, no. 3, 2012, pp. 647-697 [journal] [arXiv]
  66. Generating random density matrices (with Benoît Collins, Karol Penson and Karol Zyczkowski) – J. Math. Phys. 52, 062201 (2011) [journal] [arXiv]
  67. Random repeated quantum interactions and random invariant states (with Clément Pellegrini) – Probab. Theory Relat. Fields (2012) 152:299-320 [journal] [arXiv]
  68. Gaussianization and eigenvalue statistics for Random quantum channels (III) (with Benoît Collins) – Ann. Appl. Probab. Volume 21, Number 3 (2011), 1136-1179 [journal] [arXiv]
  69. Random quantum channels II: Entanglement of random subspaces, Rényi entropy estimates and additivity problems (with Benoît Collins) – Advances in Mathematics 226 (2011), 1181-1201 [journal] [arXiv]
  70. Eigenvalue and Entropy Statistics for Products of Conjugate Random Quantum Channels (with Benoît Collins) – Entropy (2010), 12(6), 1612-1631 [journal] [arXiv]
  71. Random graph states, maximal flow and Fuss-Catalan distributions (with Benoît Collins and Karol Zyczkowski) – J. Phys. A: Math. Theor. 43 (2010), 275303 [journal] [arXiv]
  72. Discrete approximation of the free Fock space (with Stéphane Attal) – Séminaire de Probabilités XLIII, LNM, (2011), vol. 2006/2011, 379-394 [journal] [arXiv]
  73. Random quantum channels I: graphical calculus and the Bell state phenomenon (with Benoît Collins) – Comm. Math. Phys. 297 (2010), no. 2, 345-370 [journal] [arXiv]
  74. Quantum Trajectories in Random Environment: the Statistical Model for a Heat Bath (with Clément Pellegrini) – Confluentes Mathematici, Vol. 1, No. 2 (2009), 249-289 [journal] [arXiv]
  75. A permutation model for free random variables and its classical analogue (with Florent Benaych-Georges) – Pacific Journal of Math., Vol. 242 (2009), No. 1, 33-51 [journal] [arXiv]
  76. Stochastic domination for iterated convolutions and catalytic majorization (with Guillaume Aubrun) – Ann. Inst. H. Poincaré Probab. Statist. Volume 45, Number 3 (2009), 611-625 [journal] [arXiv]
  77. Catalytic majorization and $\ell_p$ norms (with Guillaume Aubrun) – Comm. Math. Phys. 278 (2008), no. 1, 133-144 [journal] [arXiv]
  78. Asymptotics of random density matrices – Ann. Henri Poincaré 8 (2007), no. 8, 1521-1538 [journal] [arXiv]

PhD thesis

Etats aléatoires, théorie quantique de l’information et probabilités libres

  • Full text [pdf]
  • Slides [pdf]

Other memoirs

  1. Matrices densités aléatoires – July/August 2006 [pdf]
  2. Introduction à la théorie de l’information quantique – July/August 2005 [pdf]
  3. Les zéros d’une série entière gaussienne: un processus déterminantal – July/August 2004

Miscellaneous

  1. How good is a positive map at detecting quantum entanglement? – A Perspective on the paper The Non-m-Positive Dimension of a Positive Linear Map by Nathaniel Johnston, Benjamin Lovitz, and Daniel Puzzuoli, published in Quantum 3, 172 (2019) [journal]