Central Charge in Quantum Optics

• URL: http://arxiv.org/abs/2402.17114v2
• Date: Thu, 17 Oct 2024 13:56:07 GMT
• Title: Central Charge in Quantum Optics
• Abstract summary: We show that an expression in terms of a single exponential is possible only at the expense of the introduction of a new element. A quantum-optical experiment is proposed that brings to light this phenomenon.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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