Research | Cécilia Lancien | Mathematics

Research

Main research interests

Quantum information theory, Quantum many-body physics, Asymptotic geometric analysis (commutative and non-commutative), Random matrices and tensors, Free probability.

Publications and preprints

Random measurements are almost maximally incompatible (with Andreas Bluhm and Ion Nechita), preprint.
Learning mixed quantum states in large-scale experiments (with J. Ignacio Cirac, Marko Ljubotina, Lorenzo Piroli, Maksym Serbyn, Benoît Vermersch, Matteo Votto and Peter Zoller), Phys. Rev. Lett., Vol. 136, No. 9, pp. 090801 (2026).
Optimal quantum (tensor product) expanders from unitary designs, Int. Math. Res. Not., Vol. 2026, No. 2, pp. 383 (2026).
Central Limit Theorem for tensor products of free variables (with Patrick Oliveira Santos and Pierre Youssef), to appear in Can. J. Math.
Limiting spectral distribution of random self-adjoint quantum channels (with Patrick Oliveira Santos and Pierre Youssef), Math. Phys. Anal. Geom., Vol. 27, No. 3, pp. 15 (2024).
A note on quantum expanders (with Pierre Youssef), Lett. Math. Phys., Vol. 115, No. 140 (2025).
Estimating the entanglement of random multipartite quantum states (with Khurshed Fitter and Ion Nechita), Quantum, Vol. 9, No. 1870 (2025).
Random tensor networks with non-trivial links (with Newton Cheng, Geoff Penington, Michael Walter and Freek Witteveen), Ann. Henri Poincaré, Vol. 25, No. 4, pp. 2107-2212 (2024).
Multipartite entanglement detection via projective tensor norms (with Maria Anastasia Jivulescu and Ion Nechita), Ann. Henri Poincaré, Vol. 23, No. 11, pp. 3791-3838 (2022).
Characterizing expansion, classically and quantumly, Quantum Views, Vol. 4, No. 44 (2020).
Weak approximate unitary designs and applications to quantum encryption (with Christian Majenz), Quantum, Vol. 4, No. 313 (2020).
Correlation length in random MPS and PEPS (with David Pérez García), Ann. Henri Poincaré, Vol. 23, No. 1, pp. 141-222 (2022).
de Finetti reductions for partially exchangeable probability distributions (with Ivan Bardet and Ion Nechita), preprint.
Approximating quantum channels by completely positive maps with small Kraus rank (with Andreas Winter), Quantum, Vol. 8, No. 1320 (2024).
High-dimensional entanglement in states with positive partial transposition (with Marcus Huber, Ludovico Lami and Alexander Müller-Hermes), Phys. Rev. Lett., Vol. 121, No. 200503 (2018).
Random private quantum states (with Matthias Christandl and Roberto Ferrara), IEEE Trans. Inf. Th., Vol. 66, No. 7, pp. 4621-4640 (2020).
Random quantum correlations are generically non-classical (with Carlos González-Guillén, Carlos Palazuelos and Ignacio Villanueva), Ann. Henri Poincaré, Vol. 18, No. 12, pp. 3793-3813 (2017).
Flexible constrained de Finetti reductions and applications (with Andreas Winter), J. Math. Phys., Vol. 58, No. 092203 (2017).
Should entanglement measures be monogamous or faithful? (with Gerardo Adesso, Sara Di Martino, Marcus Huber, Marco Piani and Andreas Winter), Phys. Rev. Lett., Vol. 117, No. 060501 (2016).
Parallel repetition and concentration for (sub-)no-signalling games via a flexible constrained de Finetti reduction (with Andreas Winter), Chicago Journal of Theoretical Computer Science, Vol. 2016, No. 11 (2016).
k-extendibility of high-dimensional bipartite quantum states, Random Matrices Theory Appl., Vol. 5, No. 1650011 (2016).
Relaxations of separability in multipartite systems: semidefinite programs, witnesses and volumes (with Otfried Gühne, Marcus Huber and Ritabrata Sengupta), J. Phys. A: Math. Theor., Vol. 48, No. 505302 (2015).
Zonoids and sparsification of quantum measurements (with Guillaume Aubrun), Positivity, Vol. 20, No. 1, pp. 1-23 (2016).
Locally restricted measurements on a multipartite quantum system: data hiding is generic (with Guillaume Aubrun), Quant. Inf. Comput., Vol. 15, No. 5-6, pp. 512-540 (2014).
Distinguishing multi-partite states by local measurements (with Andreas Winter), Commun. Math. Phys., Vol. 323, No. 2, pp. 555-573 (2013).