Thermal Area Law for Lattice Bosons
A physical system is said to satisfy a thermal area law if the mutual information between two adjacent regions in the Gibbs state is controlled by the area of their boundary. Lattice bosons have recently gained significant interest because they can be precisely tuned in experiments and bosonic codes...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2023-08-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2023-08-16-1083/pdf/ |
| _version_ | 1797742363016167424 |
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| author | Marius Lemm Oliver Siebert |
| author_facet | Marius Lemm Oliver Siebert |
| author_sort | Marius Lemm |
| collection | DOAJ |
| description | A physical system is said to satisfy a thermal area law if the mutual information between two adjacent regions in the Gibbs state is controlled by the area of their boundary. Lattice bosons have recently gained significant interest because they can be precisely tuned in experiments and bosonic codes can be employed in quantum error correction to circumvent classical no-go theorems. However, the proofs of many basic information-theoretic inequalities such as the thermal area law break down for bosons because their interactions are unbounded. Here, we rigorously derive a thermal area law for a class of bosonic Hamiltonians in any dimension which includes the paradigmatic Bose-Hubbard model. The main idea to go beyond bounded interactions is to introduce a quasi-free reference state with artificially decreased chemical potential by means of a double Peierls-Bogoliubov estimate. |
| first_indexed | 2024-03-12T14:39:47Z |
| format | Article |
| id | doaj.art-1f109a490dae45f48b9e606ac80612f4 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-03-12T14:39:47Z |
| publishDate | 2023-08-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-1f109a490dae45f48b9e606ac80612f42023-08-16T10:57:47ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2023-08-017108310.22331/q-2023-08-16-108310.22331/q-2023-08-16-1083Thermal Area Law for Lattice BosonsMarius LemmOliver SiebertA physical system is said to satisfy a thermal area law if the mutual information between two adjacent regions in the Gibbs state is controlled by the area of their boundary. Lattice bosons have recently gained significant interest because they can be precisely tuned in experiments and bosonic codes can be employed in quantum error correction to circumvent classical no-go theorems. However, the proofs of many basic information-theoretic inequalities such as the thermal area law break down for bosons because their interactions are unbounded. Here, we rigorously derive a thermal area law for a class of bosonic Hamiltonians in any dimension which includes the paradigmatic Bose-Hubbard model. The main idea to go beyond bounded interactions is to introduce a quasi-free reference state with artificially decreased chemical potential by means of a double Peierls-Bogoliubov estimate.https://quantum-journal.org/papers/q-2023-08-16-1083/pdf/ |
| spellingShingle | Marius Lemm Oliver Siebert Thermal Area Law for Lattice Bosons Quantum |
| title | Thermal Area Law for Lattice Bosons |
| title_full | Thermal Area Law for Lattice Bosons |
| title_fullStr | Thermal Area Law for Lattice Bosons |
| title_full_unstemmed | Thermal Area Law for Lattice Bosons |
| title_short | Thermal Area Law for Lattice Bosons |
| title_sort | thermal area law for lattice bosons |
| url | https://quantum-journal.org/papers/q-2023-08-16-1083/pdf/ |
| work_keys_str_mv | AT mariuslemm thermalarealawforlatticebosons AT oliversiebert thermalarealawforlatticebosons |