Poisson Quantum Information
By taking a Poisson limit for a sequence of rare quantum objects, I derive simple formulas for the Uhlmann fidelity, the quantum Chernoff quantity, the relative entropy, and the Helstrom information. I also present analogous formulas in classical information theory for a Poisson model. An operator c...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2021-08-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2021-08-19-527/pdf/ |
| _version_ | 1819116911990931456 |
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| author | Mankei Tsang |
| author_facet | Mankei Tsang |
| author_sort | Mankei Tsang |
| collection | DOAJ |
| description | By taking a Poisson limit for a sequence of rare quantum objects, I derive simple formulas for the Uhlmann fidelity, the quantum Chernoff quantity, the relative entropy, and the Helstrom information. I also present analogous formulas in classical information theory for a Poisson model. An operator called the intensity operator emerges as the central quantity in the formalism to describe Poisson states. It behaves like a density operator but is unnormalized. The formulas in terms of the intensity operators not only resemble the general formulas in terms of the density operators, but also coincide with some existing definitions of divergences between unnormalized positive-semidefinite matrices. Furthermore, I show that the effects of certain channels on Poisson states can be described by simple maps for the intensity operators. |
| first_indexed | 2024-12-22T05:24:37Z |
| format | Article |
| id | doaj.art-865fc52ad36e49d19ce58b262290288d |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-12-22T05:24:37Z |
| publishDate | 2021-08-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-865fc52ad36e49d19ce58b262290288d2022-12-21T18:37:38ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2021-08-01552710.22331/q-2021-08-19-52710.22331/q-2021-08-19-527Poisson Quantum InformationMankei TsangBy taking a Poisson limit for a sequence of rare quantum objects, I derive simple formulas for the Uhlmann fidelity, the quantum Chernoff quantity, the relative entropy, and the Helstrom information. I also present analogous formulas in classical information theory for a Poisson model. An operator called the intensity operator emerges as the central quantity in the formalism to describe Poisson states. It behaves like a density operator but is unnormalized. The formulas in terms of the intensity operators not only resemble the general formulas in terms of the density operators, but also coincide with some existing definitions of divergences between unnormalized positive-semidefinite matrices. Furthermore, I show that the effects of certain channels on Poisson states can be described by simple maps for the intensity operators.https://quantum-journal.org/papers/q-2021-08-19-527/pdf/ |
| spellingShingle | Mankei Tsang Poisson Quantum Information Quantum |
| title | Poisson Quantum Information |
| title_full | Poisson Quantum Information |
| title_fullStr | Poisson Quantum Information |
| title_full_unstemmed | Poisson Quantum Information |
| title_short | Poisson Quantum Information |
| title_sort | poisson quantum information |
| url | https://quantum-journal.org/papers/q-2021-08-19-527/pdf/ |
| work_keys_str_mv | AT mankeitsang poissonquantuminformation |