Central Charge in Quantum Optics
Quantum Physics
2024-10-18 v2
Abstract
The product of two unitaries can normally be expressed as a single exponential through the famous Baker-Campbell-Hausdorff formula. We present here a counterexample in quantum optics, by showing that an expression in terms of a single exponential is possible only at the expense of the introduction of a new element (a central extension of the algebra), implying that there will be unitaries, generated by a sequence of gates, that cannot be generated by any time-independent quadratic Hamiltonian. A quantum-optical experiment is proposed that brings to light this phenomenon.
Cite
@article{arxiv.2402.17114,
title = {Central Charge in Quantum Optics},
author = {Daniel Burgarth and Paolo Facchi and Hiromichi Nakazato and Saverio Pascazio and Kazuya Yuasa},
journal= {arXiv preprint arXiv:2402.17114},
year = {2024}
}
Comments
13 pages, 7 figures