Infinite-Dimensional Quantum Entropy: The Unified Entropy Case
Infinite-dimensional systems play an important role in the continuous-variable quantum computation model, which can compete with a more standard approach based on qubit and quantum circuit computation models. But, in many cases, the value of entropy unfortunately cannot be easily computed for states...
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MDPI AG
2024-12-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/26/12/1070 |
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| author | Roman Gielerak Joanna Wiśniewska Marek Sawerwain |
| author_facet | Roman Gielerak Joanna Wiśniewska Marek Sawerwain |
| author_sort | Roman Gielerak |
| collection | DOAJ |
| description | Infinite-dimensional systems play an important role in the continuous-variable quantum computation model, which can compete with a more standard approach based on qubit and quantum circuit computation models. But, in many cases, the value of entropy unfortunately cannot be easily computed for states originating from an infinite-dimensional Hilbert space. Therefore, in this article, the unified quantum entropy (which extends the standard von Neumann entropy) notion is extended to the case of infinite-dimensional systems by using the Fredholm determinant theory. Some of the known (in the finite-dimensional case) basic properties of the introduced unified entropies were extended to this case study. Certain numerical examples for computing the proposed finite- and infinite-dimensional entropies are outlined as well, which allowed us to calculate the entropy values for infinite Hilbert spaces. |
| format | Article |
| id | doaj-art-77eeda1ef86e4872916c8ae8ae753ec0 |
| institution | OA Journals |
| issn | 1099-4300 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-77eeda1ef86e4872916c8ae8ae753ec02025-08-20T02:00:27ZengMDPI AGEntropy1099-43002024-12-012612107010.3390/e26121070Infinite-Dimensional Quantum Entropy: The Unified Entropy CaseRoman Gielerak0Joanna Wiśniewska1Marek Sawerwain2Institute of Control & Computation Engineering, University of Zielona Góra, Licealna 9, 65-417 Zielona Góra, PolandInstitute of Information Systems, Faculty of Cybernetics, Military University of Technology, Gen. S. Kaliskiego 2, 00-908 Warszaw, PolandInstitute of Control & Computation Engineering, University of Zielona Góra, Licealna 9, 65-417 Zielona Góra, PolandInfinite-dimensional systems play an important role in the continuous-variable quantum computation model, which can compete with a more standard approach based on qubit and quantum circuit computation models. But, in many cases, the value of entropy unfortunately cannot be easily computed for states originating from an infinite-dimensional Hilbert space. Therefore, in this article, the unified quantum entropy (which extends the standard von Neumann entropy) notion is extended to the case of infinite-dimensional systems by using the Fredholm determinant theory. Some of the known (in the finite-dimensional case) basic properties of the introduced unified entropies were extended to this case study. Certain numerical examples for computing the proposed finite- and infinite-dimensional entropies are outlined as well, which allowed us to calculate the entropy values for infinite Hilbert spaces.https://www.mdpi.com/1099-4300/26/12/1070quantum entropiesunified entropyFredholm determinantsnumerical determinants |
| spellingShingle | Roman Gielerak Joanna Wiśniewska Marek Sawerwain Infinite-Dimensional Quantum Entropy: The Unified Entropy Case Entropy quantum entropies unified entropy Fredholm determinants numerical determinants |
| title | Infinite-Dimensional Quantum Entropy: The Unified Entropy Case |
| title_full | Infinite-Dimensional Quantum Entropy: The Unified Entropy Case |
| title_fullStr | Infinite-Dimensional Quantum Entropy: The Unified Entropy Case |
| title_full_unstemmed | Infinite-Dimensional Quantum Entropy: The Unified Entropy Case |
| title_short | Infinite-Dimensional Quantum Entropy: The Unified Entropy Case |
| title_sort | infinite dimensional quantum entropy the unified entropy case |
| topic | quantum entropies unified entropy Fredholm determinants numerical determinants |
| url | https://www.mdpi.com/1099-4300/26/12/1070 |
| work_keys_str_mv | AT romangielerak infinitedimensionalquantumentropytheunifiedentropycase AT joannawisniewska infinitedimensionalquantumentropytheunifiedentropycase AT mareksawerwain infinitedimensionalquantumentropytheunifiedentropycase |