Higher moment theory and learnability of bosonic states

Abstract:We present a sample- and time-efficient algorithm to learn any bosonic Fock state acted upon by an arbitrary Gaussian unitary. As a special case, this algorithm efficiently learns states produced in Fock state BosonSampling, thus resolving an open question put forth by Aaronson and Grewal (Aaronson, Grewal 2023). We further study a hierarchy of classes of states beyond Gaussian states that are specified by a finite number of their higher moments. Using the higher moments, we find a full spectrum of invariants under Gaussian unitaries, thereby providing necessary conditions for two states to be related by an arbitrary (including active, e.g. beyond linear optics) Gaussian unitary.

9+21 pages, 1 figure. Bounds have been improved for V2

arXiv:2510.01610 [quant-ph]

(or arXiv:2510.01610v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2510.01610 Focus to learn more arXiv-issued DOI via DataCite

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