Central Charge in Quantum Optics
Abstract
The product of two unitaries can normally be expressed as a single exponential through the famous BakerCampbellHausdorff 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 timeindependent quadratic Hamiltonian. A quantumoptical experiment is proposed that brings to light this phenomenon.
 Publication:

arXiv eprints
 Pub Date:
 February 2024
 DOI:
 10.48550/arXiv.2402.17114
 arXiv:
 arXiv:2402.17114
 Bibcode:
 2024arXiv240217114B
 Keywords:

 Quantum Physics
 EPrint:
 12 pages, 7 figures