Speaker: Francesco Anna Mele (SNS Pisa)
Title: From tomography of bosonic systems to a new measure of non-Gaussianity: the symplectic rank
Abstract: Quantum state tomography, aimed at deriving a classical description of an unknown state from measurement data, is a fundamental task in quantum physics. In parallel, non-Gaussianity serves as a crucial resource for quantum information processing in continuous-variable (CV) systems. In this talk, we investigate the fundamental limits of quantum state tomography for CV systems, revealing a deep connection between the efficiency in tomography and the degree of non-Gaussianity. Specifically:
- We first show that tomography of general non-Gaussian states is extremely inefficient;
- In contrast, we demonstrate that tomography of Gaussian states is efficient. To accomplish this, we introduce new tools of independent interest: tight bounds on the trace distance between CV states in terms of the norm distance between their first moments and covariance matrices.
- We then explore the intermediate regime, establishing that tomography becomes progressively harder as the level of non-Gaussianity increases.
The latter result naturally leads to the concept of symplectic rank: a novel non-Gaussianity monotone that satisfies remarkable operational and resource-theoretic properties. Mathematically, the symplectic rank of a pure state is the number of symplectic eigenvalues of the covariance matrix that are strictly larger than the ones of the vacuum. Importantly, the symplectic rank is non-increasing under post-selected Gaussian operations, leading to strictly stronger no-go theorems for Gaussian conversion than those previously known.
The talk will be based on: https://arxiv.org/pdf/2405.01431, https://arxiv.org/pdf/2411.02368, https://arxiv.org/abs/2508.14979v1, and https://arxiv.org/pdf/2504.19319.
About: Weekly seminar of the Quantum Working Group, covering topics in quantum information theory and operator algebras. Contact Marius Junge (mjunge@illinois.edu), Felix Leditzky (leditzky@illinois.edu), or Amanda Young (ayoung86@illinois.edu) with questions or inquiries.