Central Charge in Quantum Optics

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.

13 pages, 7 figures

References in corpus (11)

• Anyons in an exactly solved model and beyond
• Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency
• Zoo of quantum-topological phases of matter
• Continuous variable quantum information: Gaussian states and beyond
• Covariant theory of asymptotic symmetries, conservation laws and central charges
• Anyons and the quantum Hall effect - a pedagogical review
• Quantum Zeno dynamics: mathematical and physical aspects
• Boundary Conformal Field Theory and a Boundary Central Charge
• String theory on ${\text{AdS}}_3$ and the symmetric orbifold of Liouville theory
• Chiral central charge from a single bulk wave function
• Generalized Product Formulas and Quantum Control