A fundamental task in quantum metrology is to identify the ultimate sensitivity limit in the estimation of a parameter encoded into a quantum state. Even under ideal conditions, when all technical noise sources are removed, quantum noise poses unavoidable limitations to such estimation. In spite of that, quantum parameter estimation theory provides the tools to reduce noise by optimizing the output measurements. This optimization leads to the quantum Cramér-Rao lower bound, which gives the minimal uncertainty of the estimator of a parameter, and that can be further optimized by finding quantum states that, for a given parameter, maximize the value of the quantum Fisher information.

In the optical scenario, would it be in imaging, remote sensing or interferometric measurement, the parameter of interest does not only modify the quantum state of the probe light, but also its spatio-temporal distribution. This distribution is conveniently described in terms of modes i.e. normalized solutions of Maxwell’s equations in vacuum [1]. Optimal quantum parameter estimation is thus at the crossroads between quantum information theory and optical mode manipulation, where only by taking into account both classical and quantum optimization one can derive efficient and practical estimators.

The multimode quantum optics group of Laboratoire Kastler Brossel, pioneered many aspects of optical quantum parameter estimation, in particular in the continuous variable (CV) approach [2,3]. Our activities generally span both spatial and spectral modes, which we manipulate to develop tools for quantum computation, communication, and metrology. The group has a strong experimental focus, but also has purely theoretical activities where the framework of CV quantum optics is further developed. The interplay between theoretical work and experiments is a key element of our group.


When dealing with extracting a few parameters from an image, using prior information allows for going far beyond the Rayleigh limit. In practice, this can be achieved using the correlation of electromagnetic field amplitudes at different transverse positions of the image plane, and not only the intensity distribution. Technically, this involves decomposing the incoming field into an orthonormal basis of spatial modes (typically, Hermite-Gaussian) and measuring the amplitude (or intensity) of each basis component. This method of spatial demultiplexing, or SpaDe [4], enables us to not only achieve sub-Rayleigh precision, but also, in some cases, reach the ultimate resolution limits allowed by quantum mechanics [5,6]. The objectives of the group are to:

  • Determine the physical limits of multi-parameter estimation to quantum estimation theory.
  • Demonstrate practical parameter estimation with mode demultiplexing
  • Implement a Bayesian framework for static and dynamic superresolution imaging.

Furthermore, the group has an ongoing collaboration with Thales Research and Technology to study distant imaging with frequency conversion, whose aim is to bring the system to new applications.

The postdoctoral fellow will have to coordinate the group activities in optical parameter estimation to reach the above objectives. She/He will have a background either in theoretical or experimental physics, but an interest to combine both in order to bring modal approach to parameter estimation to a practical device and to apprehend the fundamental limits imposed by the quantum nature of light in multi-parameter estimation in the presence of experimental imperfection. The work can have extension either in the more fundamental studies of the group, in particular regarding the link between Quantum Fisher information and quantum non-gaussian states of light [7], or to more practical considerations in particular within the framework of the collaboration with Thales.


As a whole, the group has a tradition of working together with a diverse range of people from very varied backgrounds. This diversity often leads to fruitful scientific input from different points of view, and it allows the group to explore new avenues. This has, for example, led to a growing activity in theoretical work over the past few years. The strength of our group is the constructive interplay between all these different points of view.  Furthermore, the moderate size of our group gives PhD students and postdocs the opportunity to discuss with PIs on a daily basis. This gives rise to a dynamical atmosphere with a lot of space for discussion.

In your day-to-day activities, you will supervise PhD students who work on the same activity, and you are responsible for the everyday organization of the work. You will be involved in several European programs, which will enlarge your scientific network and provide opportunities for international collaborations.

  • Application process: Send CV and motivation letter to nicolas.treps@sorbonne-universite.fr
  • Application deadline: Preferentially apply before 31st of March 2023  (late application will be considered as long as the position has not been filled).


[1]        C. Fabre and N. Treps, Modes and states in quantum optics. Rev. Mod. Phys. 92, 035005 (2020). https://doi.org/10.1103/RevModPhys.92.035005

[2]        N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, A Quantum Laser Pointer, Science 301, 940 (2003).

[3]        O. Pinel, J. Fade, D. Braun, P. Jian, N. Treps, C. Fabre, Ultimate sensitivity of precision measurements with in- tense Gaussian quantum light: a multi-modal approach, Phys. Rev. A 85, 010101(R) (2012). https://journals.aps.org/pra/abstract/10.1103/PhysRevA.85.010101

[4]        Labroille, G. et al. Efficient and mode selective spatial mode multiplexer based on multi-plane light conversion. Opt. Express 22, 15599–15607 (2014). https://doi.org/10.1364/OE.22.015599

[5]        Tsang, M., Nair, R. & Lu, X.-M. Quantum theory of superresolution for two incoherent optical point sources. Phys. Rev. X 6, 031033 (2016). URL https://link.aps.org/doi/10.1103/PhysRevX.6.031033 .

[6]        P. Boucher, C. Fabre, G. Labroille, and N. Treps, Spatial Optical Mode Demultiplexing as a Practical Tool for Optimal Transverse Distance Estimation, Optica, OPTICA 7, 1621 (2020). https://doi.org/10.1364/OPTICA.404746

[7]        C. E. Lopetegui, M. Gessner, M. Fadel, N. Treps, and M. Walschaers, Homodyne Detection of Non-Gaussian Quantum Steering, PRX Quantum 3, 030347 (2022). https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.3.030347


Research Field
Physics » Quantum mechanics
Education Level
PhD or equivalent