Mainz 2026 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 78: Quantum Optics and Control III
Q 78.3: Talk
Friday, March 6, 2026, 15:00–15:15, P 3
Density matrx estimation of multi-mode quantum states from incomplete homodyne data — •Isabell Mischke1, Carlos Lopetegui2, Bastien Oriot2, Mattia Walschaers2, Valentina Parigi2, and Tim J. Bartley1, 3 — 1Department of Physics, Paderborn University, Warburger Str. 100, 33098 Paderborn, Germany — 2Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France, 4 place Jussieu, F-75252, Paris, France — 3Institue for Photonic Quantum Systems (PhoQS), Paderborn UNiversity, Warburger Str. 100, 33098 Paderborn, Germany
Homodyne tomography is an experimental procedure to characterize for instance non-classical states as it allows us to determine the state*s statistical operator. The maximum likelihood estimation (MLE) is one possibility to recreate the density matrix from the experimental homodyne quadrature data by finding the most-likely matrix that could have produced the data. The reconstruction itself is a computationally demanding task with exponential scaling for an ascending number of modes. More degrees of freedom become increasingly relevant when looking at highly entangled systems such as cluster states.
We investigate whether it is possible to completely identify the density matrix of a multi-mode state when only a subset of modes is experimentally accessible. With a semidefinite programming approach, we are working towards the approximation of the density matrix by reducing the necessary computational time compared to the analysis of the data of the whole multi-mode state. In the future this method might enable the reconstruction of states with more than four modes.
Keywords: Homodyne detection; Quantum state tomography; Maximum likelihood estimation; Multi-mode states; Density matrix approximation