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  • Letter
  • Open Access

Central charge in quantum optics

Daniel Burgarth1, Paolo Facchi2,3, Hiromichi Nakazato4, Saverio Pascazio2,3, and Kazuya Yuasa4

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Phys. Rev. Research 6, L042011 – Published 10 October, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L042011

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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Phys. Rev. Research 6, L042011– Published 10 October, 2024
  • Received 28 February 2024
  • Accepted 13 September 2024
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