Central charge in quantum optics

Daniel Burgarth

doi:10.1103/PhysRevResearch.6.L042011

Central charge in quantum optics

2024-10-10

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DOI：10.1103/PhysRevResearch.6.L042011

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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.

Keywords:

HAUSDORFF

CAMPBELL

ANYONS

BAKER

Central charge in quantum optics

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