# Research

**Interests** [WordCloud]

- Probability theory
- Free probability theory
- Quantum information theory

**Funding**

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

**Papers**

Recent preprints

- A graphical calculus for integration over random diagonal unitary matrices (with Satvik Singh) [arXiv]
- SudoQ – a quantum variant of the popular game (with Jordi Pillet) [arXiv]
- Sinkhorn algorithm for quantum permutation groups (with Simon Schmidt and Moritz Weber) [arXiv]
- A refinement of Reznick’s Positivstellensatz with applications to quantum information theory (with Alexander Müller-Hermes and David Reeb) [arXiv]
- On the spectral gap of random quantum channels (with Carlos E. González-Guillén and Marius Junge) [arXiv]
- de Finetti reductions for partially exchangeable probability distributions (with Ivan Bardet and Cécilia Lancien) [arXiv]

Published/accepted papers

- Random positive operator valued measures (with Teiko Heinosaari and Maria Jivulescu) – Journal of Mathematical Physics 61, 042202 (2020) [journal] [arXiv]
- 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]
- 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]
- 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]
- Joint measurability of quantum effects and the matrix diamond (with Andreas Bluhm) – Journal of Mathematical Physics 59, 112202 (2018) [journal] [arXiv]
- Operator Schmidt ranks of bipartite unitary matrices (with Alexander Müller-Hermes) – Lin. Alg. and its Appl. 557, 174-187 (2018) [journal] [arXiv]
- On the separability of unitarily invariant random quantum states – the unbalanced regime – Adv. Math. Phys., vol. 2018, Article ID 7105074 (2018) [journal] [arXiv]
- Almost all quantum channels are equidistant (with Zbigniew Puchała, Łukasz Pawela, Karol Życzkowski) – Journal of Mathematical Physics 59, 052201 (2018) [journal] [arXiv]
- 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]
- Enumerating meandric systems with large number of components (with Motohisa Fukuda) – Ann. Inst. Henri Poincaré D, 6, 4, 607-640 (2019) [journal] [arXiv]
- Almost Hadamard matrices with complex entries (with Teodor Banica) – Adv. Oper. Theory 3, no. 1, 149–189 (2018) [journal] [arXiv]
- On symmetric decompositions of positive operators (with Maria Jivulescu and Pasc Gavruta) – J. Phys. A: Math. Theor. 50 165303 (2017) [journal] [arXiv]
- On bipartite unitary matrices generating subalgebra-preserving quantum operations (with Tristan Benoist) – Linear Algebra and its Applications 521, 70–103 (2017) – [journal] [arXiv]
- Flat matrix models for quantum permutation groups (with Teodor Banica) – Adv. Appl. Math. 83, 24-46 (2017) [journal] [arXiv]
- On some classes of bipartite unitary operators (with Julien Deschamps and Clément Pellegrini) – J. Phys. A: Math. Theor. 49 335301 (2016) [journal] [arXiv]
- Random and free positive maps with applications to entanglement detection (with Benoit Collins and Patrick Hayden) – International Mathematics Research Notices, rnw054 (2016) [journal] [arXiv]
- On the asymptotic distribution of block-modified random matrices (with Octavio Arizmendi and Carlos Vargas) – Journal of Mathematical Physics 57, 015216 (2016) [journal] [arXiv]
- Random matrix techniques in quantum information theory (with Benoit Collins) – Journal of Mathematical Physics 57, 015215 (2016) [journal] [arXiv]
- 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]
- 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]
- Additivity rates and PPT property for random quantum channels (with Motohisa Fukuda) – Ann. Math. Blaise Pascal 22, 1-72 (2015) [journal] [arXiv]
- 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]
- 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]
- Positive reduction from spectra (with Maria Anastasia Jivulescu, Nicolae Lupa, and David Reeb) – Linear Algebra and its Applications 469 (2015) 276–304 [journal] [arXiv]
- On the reduction criterion for random quantum states (with Maria Anastasia Jivulescu and Nicolae Lupa) – J. Math. Phys. 55, 112203 (2014) [journal] [arXiv]
- Analytic aspects of the circulant Hadamard conjecture (with Teodor Banica and Jean-Marc Schlenker) – Ann. Math. Blaise Pascal 21 (2014), 25-59 [journal] [arXiv]
- 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]
- 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]
- Submatrices of Hadamard matrices: complementation results (with Teodor Banica and Jean-Marc Schlenker) – Electron. J. Linear Algebra 27 (2014), 197-212 [journal] [arXiv]
- Area law for random graph states (with Benoît Collins and Karol Zyczkowski) – J. Phys. A: Math. Theor. 46 305302 (2013) [journal] [arXiv]
- Almost Hadamard matrices: the case of arbitrary exponents (with Teodor Banica) – Discrete Applied Mathematics, vol. 161, no. 16–17, 2367-2379 (2013) [journal] [arXiv]
- Random pure quantum states via unitary Brownian motion (with Clément Pellegrini) – Electron. Commun. Probab. 18 (2013), no. 27, 1–13 [journal] [arXiv]
- 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]
- 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]
- Realigning random states (with Guillaume Aubrun) – J. Math. Phys. 53, 102210 (2012) [journal] [arXiv]
- Block-modified Wishart matrices and free Poisson laws (with Teodor Banica) – Houston Journal of Mathematics, Volume 41, No. 1 (2015) [journal] [arXiv]
- 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]
- 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]
- 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]
- Asymptotic eigenvalue distributions of block-transposed Wishart matrices (with Teodor Banica) – J. Theoret. Probab. 26 (2013), 855-869 [journal] [arXiv]
- 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]
- Generating random density matrices (with Benoît Collins, Karol Penson and Karol Zyczkowski) – J. Math. Phys. 52, 062201 (2011) [journal] [arXiv]
- Random repeated quantum interactions and random invariant states (with Clément Pellegrini) – Probab. Theory Relat. Fields (2012) 152:299-320 [journal] [arXiv]
- Gaussianization and eigenvalue statistics for Random quantum channels (III) (with Benoît Collins) – Ann. Appl. Probab. Volume 21, Number 3 (2011), 1136-1179 [journal] [arXiv]
- 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]
- Eigenvalue and Entropy Statistics for Products of Conjugate Random Quantum Channels (with Benoît Collins) – Entropy (2010), 12(6), 1612-1631 [journal] [arXiv]
- 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]
- Discrete approximation of the free Fock space (with Stéphane Attal) – Séminaire de Probabilités XLIII, LNM, (2011), vol. 2006/2011, 379-394 [journal] [arXiv]
- 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]
- 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]
- 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]
- 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]
- Catalytic majorization and $$\ell_p$$ norms (with Guillaume Aubrun) – Comm. Math. Phys. 278 (2008), no. 1, 133-144 [journal] [arXiv]
- 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

**Schooling**

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

**Miscellaneous**

- 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
- Annales Henri Poincaré
- Electronic Journal of Probability
- Communications in Mathematical Physics
- Bernoulli
- Entropy
- Journal of Mathematical Physics
- Physical Reviews A
- Probability Theory and Related Fields
- Quantum Information and Computation
- International Mathematics Research Notices (IMRN)
- 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)

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