Work

Testing bosonic and fermionic Gaussian states with a constant number of copies

Year: 2026

Type: preprint

Abstract: Bosonic and fermionic Gaussian quantum states are families of quantum states that play a central role in quantum physics and quantum information processing. We study the problem of testing whether a given state is either Gaussian, or has bounded overlap with any Gaussian state. Previous analyses of this testing problem led to tests that require a number of copies of the state that scales with the number of modes (the system size). In this work we show that a constant number of copies of the state suffices. We derive these results based on the symmetries of identical copies of Gaussian states, and by bounding the distance to the set of Gaussian states through a gradient flow and a spectral bound studied previously for the Kac random walk on a sphere.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.06794

Authors: Briët, Jop, Castro-Silva, Davi, Walter, Michael, Witteveen, Freek

Institutions: Leiden University, Centrum Wiskunde & Informatica, QuSoft, University of Warwick, University of Amsterdam, Ludwig-Maximilians-Universität München

Language: English

Topic: Quantum Information and Cryptography

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, Deutsche Forschungsgemeinschaft, Klaus Tschira Stiftung, Simons Institute for the Theory of Computing, University of California Berkeley

Awards: G1768993395, G8338656773, EXC 2111: Munich Center for Quantum Science and Technology (MCQST)

OpenAlex ID: W7220714195

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