| Download | - View final version: Covariant operator bases for continuous variables (PDF, 1020 KiB)
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| DOI | Resolve DOI: https://doi.org/10.22331/q-2024-05-29-1363 |
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| Author | Search for: Goldberg, A. Z.1ORCID identifier: https://orcid.org/0000-0002-3301-7672; Search for: Klimov, A. B.; Search for: Leuchs, G.; Search for: Sanchez-Soto, L. L. |
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| Affiliation | - National Research Council of Canada. Quantum and Nanotechnologies
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| Funder | Search for: European Union Horizon 2020; Search for: Agencia Española de Investigacion |
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| Format | Text, Article |
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| Subject | quantum theory; number; Gaussian distriution |
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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. |
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| Publication date | 2024-05-29 |
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| Publisher | Association for the promotion of open access publishing in quantum science |
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| Licence | |
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| In | |
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| Language | English |
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| Peer reviewed | Yes |
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| Export citation | Export as RIS |
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| Report a correction | Report a correction (opens in a new tab) |
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| Record identifier | 450a1fa6-3b57-42bc-b32c-67b568f0edfe |
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| Record created | 2024-09-12 |
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| Record modified | 2024-09-12 |
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