Interests

  • Probability theory
  • Free probability theory
  • Quantum information theory

Funding

  • STOQ – member, ANR Blanc
  • RMTQIT – coordinator, ANR Blanc International
  • OSQPI – member, ANR Blanc

Papers [arXiv]

Published/accepted papers

  1. Quantum channels with polytopic images and image additivity (with Motohisa Fukuda, and Michael M. Wolf) – to appear in IEEE Transactions on Information Theory
  2. Positive reduction from spectra (with Maria Anastasia Jivulescu, Nicolae Lupa, and David Reeb) – Linear Algebra and its Applications 469 (2015) 276–304
  3. On the reduction criterion for random quantum states (with Maria Anastasia Jivulescu and Nicolae Lupa) – J. Math. Phys. 55, 112203 (2014)
  4. Analytic aspects of the circulant Hadamard conjecture (with Teodor Banica and Jean-Marc Schlenker) – Ann. Math. Blaise Pascal 21 (2014), 25-59
  5. 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
  6. 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
  7. Submatrices of Hadamard matrices: complementation results (with Teodor Banica and Jean-Marc Schlenker) – Electron. J. Linear Algebra 27 (2014), 197-212.
  8. Area law for random graph states (with Benoît Collins and Karol Zyczkowski) – J. Phys. A: Math. Theor. 46 305302 (2013)
  9. Almost Hadamard matrices: the case of arbitrary exponents (with Teodor Banica) – Discrete Applied Mathematics, vol. 161, no. 16–17, 2367-2379 (2013)
  10. Random pure quantum states via unitary Brownian motion (with Clément Pellegrini) – Electron. Commun. Probab. 18 (2013), no. 27, 1–13.
  11. Low entropy output states for products of random unitary channels (with Benoit Collins and Motohisa Fukuda) – Random Matrices: Theory Appl. 02, 1250018 (2013).
  12. Almost Hadamard matrices: general theory and examples (with Teodor Banica and Karol Zyczkowski) – Open Systems & Information Dynamics, Vol. 19, No. 4, 1250024 (2012)
  13. Realigning random states (with Guillaume Aubrun) – J. Math. Phys. 53, 102210 (2012)
  14. Block-modified Wishart matrices and free Poisson laws (with Teodor Banica) – Houston Journal of Mathematics, Volume 41, No. 1 (2015)
  15. The absolute positive partial transpose property for random induced states (with Benoît Collins and Deping Ye) – Random Matrices: Theory Appl. 01, 1250002 (2012)
  16. 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)
  17. The multiplicative property characterizes $\ell_p$ and $L_p$ norms (with Guillaume Aubrun) – Confluentes Mathematici, Volume 3, Number 4 (2011), pp. 637-647
  18. Asymptotic eigenvalue distributions of block-transposed Wishart matrices (with Teodor Banica) – J. Theoret. Probab. 26 (2013), 855-869
  19. Laws of large numbers for eigenvectors and eigenvalues associated to random subspaces in a tensor product (with Benoît Collins and Serban Belinschi) – Inventiones mathematicae, vol. 190, no. 3, 2012, pp. 647-697
  20. Generating random density matrices (with Benoît Collins, Karol Penson and Karol Zyczkowski) – J. Math. Phys. 52, 062201 (2011)
  21. Random repeated quantum interactions and random invariant states (with Clément Pellegrini) – Probab. Theory Relat. Fields (2012) 152:299-320
  22. Gaussianization and eigenvalue statistics for Random quantum channels (III) (with Benoît Collins) – Ann. Appl. Probab. Volume 21, Number 3 (2011), 1136-1179
  23. Random quantum channels II: Entanglement of random subspaces, Rényi entropy estimates and additivity problems (with Benoît Collins) – Advances in Mathematics 226 (2011), 1181-1201
  24. Eigenvalue and Entropy Statistics for Products of Conjugate Random Quantum Channels (with Benoît Collins) – Entropy (2010), 12(6), 1612-1631
  25. Random graph states, maximal flow and Fuss-Catalan distributions (with Benoît Collins and Karol Zyczkowski) – J. Phys. A: Math. Theor. 43 (2010), 275303
  26. Discrete approximation of the free Fock space (with Stéphane Attal) – Séminaire de Probabilités XLIII, LNM, (2011), vol. 2006/2011, 379-394
  27. Random quantum channels I: graphical calculus and the Bell state phenomenon (with Benoît Collins) – Comm. Math. Phys. 297 (2010), no. 2, 345-370
  28. Quantum Trajectories in Random Environment: the Statistical Model for a Heat Bath (with Clément Pellegrini) – Confluentes Mathematici, Vol. 1, No. 2 (2009), 249-289
  29. 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
  30. Stochastic domination for iterated convolutions and catalytic majorization (with Guillaume Aubrun) – Ann. Inst. H. Poincaré Probab. Statist. Volume 45, Number 3 (2009), 611-625
  31. Catalytic majorization and $\ell_p$ norms (with Guillaume Aubrun) – Comm. Math. Phys. 278 (2008), no. 1, 133-144
  32. Asymptotics of random density matrices – Ann. Henri Poincaré 8 (2007), no. 8, 1521-1538

Work in progress/submitted

  1. Almost one bit violation for the additivity of the minimum output entropy (with Benoit Collins and Serban Belinschi)
  2. On the convergence of output sets of quantum channels (with Benoit Collins and Motohisa Fukuda)
  3. Additivity rates and PPT property for random quantum channels (with Motohisa Fukuda)

PhD thesis

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

  • Full text [pdf]
  • Slides [pdf]

Schooling

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

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
  • Referee for NSERC Discovery grants
  • Report writer for AMS Mathematical Reviews (Mathscinet)