Covariant operator bases for continuous variables

A. Z. Goldberg; A. B. Klimov; G. Leuchs; L. L. Sanchez-Soto

doi:10.22331/q-2024-05-29-1363

Covariant operator bases for continuous variables

A. Z. Goldberg^1,2, A. B. Klimov³, G. Leuchs⁴, and L. L. Sanchez-Soto^4,5

¹National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario K1N 5A2, Canada
²Department of Physics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
³Departamento de Física, Universidad de Guadalajara, 44420 Guadalajara, Jalisco, Mexico
⁴Max-Planck-Institut für die Physik des Lichts, 91058 Erlangen, Germany
⁵Departamento de Óptica, Facultad de Física, Universidad Complutense, 28040 Madrid, Spain

Published:	2024-05-29, volume 8, page 1363
Eprint:	arXiv:2309.10042v2
Doi:	https://doi.org/10.22331/q-2024-05-29-1363
Citation:	Quantum 8, 1363 (2024).

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Abstract

Coherent-state representations are a standard tool to deal with continuous-variable systems, as they allow one to efficiently visualize quantum states in phase space. Here, we work out an alternative basis consisting of monomials on the basic observables, with the crucial property of behaving well under symplectic transformations. This basis is the analogue of the irreducible tensors widely used in the context of SU(2) symmetry. Given the density matrix of a state, the expansion coefficients in that basis constitute the multipoles, which describe the state in a canonically covariant form that is both concise and explicit. We use these quantities to assess properties such as quantumness or Gaussianity and to furnish direct connections between tomographic measurements and quasiprobability distribution reconstructions.

► BibTeX data

@article{Goldberg2024covariantoperator,
  doi = {10.22331/q-2024-05-29-1363},
  url = {https://doi.org/10.22331/q-2024-05-29-1363},
  title = {Covariant operator bases for continuous variables},
  author = {Goldberg, A. Z. and Klimov, A. B. and Leuchs, G. and Sanchez-Soto, L. L.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1363},
  month = may,
  year = {2024}
}

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