Interests [WordCloud]

  • Probability theory
  • Free probability theory
  • Quantum information theory


  • PHC Sakura Random Matrices and Tensors for Quantum Information and Machine Learning, PI France, 2020-2021


Recent preprints

  1. Sinkhorn algorithm for quantum permutation groups (with Simon Schmidt and Moritz Weber) [arXiv]
  2. A refinement of Reznick's Positivstellensatz with applications to quantum information theory (with Alexander Müller-Hermes and David Reeb) [arXiv]
  3. Random positive operator valued measures (with Teiko Heinosaari and Maria Jivulescu) [arXiv]
  4. On the spectral gap of random quantum channels (with Carlos E. González-Guillén and Marius Junge) [arXiv]
  5. Compatibility of quantum measurements and inclusion constants for the matrix jewel (with Andreas Bluhm) [arXiv]
  6. de Finetti reductions for partially exchangeable probability distributions (with Ivan Bardet and Cécilia Lancien) [arXiv]

Published/accepted papers

  1. 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]
  2. On the joint distribution of the marginals of multipartite random quantum states (with Stephane Dartois and Luca Lionni) - to appear in Random Matrices: Theory and Applications [journal] [arXiv]
  3. Joint measurability of quantum effects and the matrix diamond (with Andreas Bluhm) - Journal of Mathematical Physics 59, 112202 (2018) [journal] [arXiv]
  4. Operator Schmidt ranks of bipartite unitary matrices (with Alexander Müller-Hermes) - Lin. Alg. and its Appl. 557, 174-187 (2018) [journal] [arXiv]
  5. On the separability of unitarily invariant random quantum states - the unbalanced regime - Adv. Math. Phys., vol. 2018, Article ID 7105074 (2018) [journal] [arXiv]
  6. Almost all quantum channels are equidistant (with Zbigniew Puchała, Łukasz Pawela, Karol Życzkowski) - Journal of Mathematical Physics 59, 052201 (2018) [journal] [arXiv]
  7. 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]
  8. Enumerating meandric systems with large number of components (with Motohisa Fukuda) - Ann. Inst. Henri Poincaré D, 6, 4, 607-640 (2019) [journal] [arXiv]
  9. Almost Hadamard matrices with complex entries (with Teodor Banica) - Adv. Oper. Theory 3, no. 1, 149–189 (2018) [journal] [arXiv]
  10. On symmetric decompositions of positive operators (with Maria Jivulescu and Pasc Gavruta) - J. Phys. A: Math. Theor. 50 165303 (2017) [journal] [arXiv]
  11. On bipartite unitary matrices generating subalgebra-preserving quantum operations (with Tristan Benoist) - Linear Algebra and its Applications 521, 70–103 (2017) - [journal] [arXiv]
  12. Flat matrix models for quantum permutation groups (with Teodor Banica) - Adv. Appl. Math. 83, 24-46 (2017) [journal] [arXiv]
  13. On some classes of bipartite unitary operators (with Julien Deschamps and Clément Pellegrini) - J. Phys. A: Math. Theor. 49 335301 (2016) [journal] [arXiv]
  14. Random and free positive maps with applications to entanglement detection (with Benoit Collins and Patrick Hayden) - International Mathematics Research Notices, rnw054 (2016) [journal] [arXiv]
  15. On the asymptotic distribution of block-modified random matrices (with Octavio Arizmendi and Carlos Vargas) - Journal of Mathematical Physics 57, 015216 (2016) [journal] [arXiv]
  16. Random matrix techniques in quantum information theory (with Benoit Collins) - Journal of Mathematical Physics 57, 015215 (2016) [journal] [arXiv]
  17. 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]
  18. 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]
  19. Additivity rates and PPT property for random quantum channels (with Motohisa Fukuda) - Ann. Math. Blaise Pascal 22, 1-72 (2015) [journal] [arXiv]
  20. 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]
  21. 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]
  22. Positive reduction from spectra (with Maria Anastasia Jivulescu, Nicolae Lupa, and David Reeb) - Linear Algebra and its Applications 469 (2015) 276–304 [journal] [arXiv]
  23. On the reduction criterion for random quantum states (with Maria Anastasia Jivulescu and Nicolae Lupa) - J. Math. Phys. 55, 112203 (2014) [journal] [arXiv]
  24. Analytic aspects of the circulant Hadamard conjecture (with Teodor Banica and Jean-Marc Schlenker) - Ann. Math. Blaise Pascal 21 (2014), 25-59 [journal] [arXiv]
  25. 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]
  26. 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]
  27. Submatrices of Hadamard matrices: complementation results (with Teodor Banica and Jean-Marc Schlenker) - Electron. J. Linear Algebra 27 (2014), 197-212 [journal] [arXiv]
  28. Area law for random graph states (with Benoît Collins and Karol Zyczkowski) - J. Phys. A: Math. Theor. 46 305302 (2013) [journal] [arXiv]
  29. Almost Hadamard matrices: the case of arbitrary exponents (with Teodor Banica) - Discrete Applied Mathematics, vol. 161, no. 16–17, 2367-2379 (2013) [journal] [arXiv]
  30. Random pure quantum states via unitary Brownian motion (with Clément Pellegrini) - Electron. Commun. Probab. 18 (2013), no. 27, 1–13 [journal] [arXiv]
  31. 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]
  32. 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]
  33. Realigning random states (with Guillaume Aubrun) - J. Math. Phys. 53, 102210 (2012) [journal] [arXiv]
  34. Block-modified Wishart matrices and free Poisson laws (with Teodor Banica) - Houston Journal of Mathematics, Volume 41, No. 1 (2015) [journal] [arXiv]
  35. 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]
  36. 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]
  37. 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]
  38. Asymptotic eigenvalue distributions of block-transposed Wishart matrices (with Teodor Banica) - J. Theoret. Probab. 26 (2013), 855-869 [journal] [arXiv]
  39. 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]
  40. Generating random density matrices (with Benoît Collins, Karol Penson and Karol Zyczkowski) - J. Math. Phys. 52, 062201 (2011) [journal] [arXiv]
  41. Random repeated quantum interactions and random invariant states (with Clément Pellegrini) - Probab. Theory Relat. Fields (2012) 152:299-320 [journal] [arXiv]
  42. Gaussianization and eigenvalue statistics for Random quantum channels (III) (with Benoît Collins) - Ann. Appl. Probab. Volume 21, Number 3 (2011), 1136-1179 [journal] [arXiv]
  43. 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]
  44. Eigenvalue and Entropy Statistics for Products of Conjugate Random Quantum Channels (with Benoît Collins) - Entropy (2010), 12(6), 1612-1631 [journal] [arXiv]
  45. 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]
  46. Discrete approximation of the free Fock space (with Stéphane Attal) - Séminaire de Probabilités XLIII, LNM, (2011), vol. 2006/2011, 379-394 [journal] [arXiv]
  47. 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]
  48. 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]
  49. 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]
  50. 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]
  51. Catalytic majorization and norms (with Guillaume Aubrun) - Comm. Math. Phys. 278 (2008), no. 1, 133-144 [journal] [arXiv]
  52. 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]


  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


  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]

Peer reviewing

  • Referee for the following journals
    1. Annales Henri Poincaré
    2. Electronic Journal of Probability
    3. Communications in Mathematical Physics
    4. Bernoulli
    5. Entropy
    6. Journal of Mathematical Physics
    7. Physical Reviews A
    8. Probability Theory and Related Fields
    9. Quantum Information and Computation
    10. International Mathematics Research Notices (IMRN)
    11. Journal of Physics A
  • Referee for the CNRS, NSERC (Canada), National Science Center (Poland), FWF Der Wissenschaftsfonds (Austria)
  • Report writer for AMS Mathematical Reviews (Mathscinet)