Quantum Filtering at Finite Temperature
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911365273223168 |
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| author | Gough, John |
| author_facet | Gough, John |
| contents | We pose and solve the problem of quantum filtering based on continuous-in-time quadrature measurements (homodyning) for the case where the quantum process is in a thermal state. The standard construction of quantum filters involves the determination of the conditional expectation onto the von Neumann algebra generated by the measured observables with the non-demolition principle telling us to restrict the domain (the observables to be estimated) to the commutant of the algebra. The finite-temperature case, however, has additional structure: we use the Araki-Woods representation for the measured quadratures, but the Tomita-Takesaki theory tells us that there exists a separate, commuting representation and therefore the commutant will have a richer structure than encountered in the Fock vacuum case. We apply this to the question of quantum trajectories to the Davies-Fulling-Unruh model. Here, the two representations are interpreted as the fields in the right and left Rindler wedges. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_04967 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Filtering at Finite Temperature Gough, John Quantum Physics Mathematical Physics We pose and solve the problem of quantum filtering based on continuous-in-time quadrature measurements (homodyning) for the case where the quantum process is in a thermal state. The standard construction of quantum filters involves the determination of the conditional expectation onto the von Neumann algebra generated by the measured observables with the non-demolition principle telling us to restrict the domain (the observables to be estimated) to the commutant of the algebra. The finite-temperature case, however, has additional structure: we use the Araki-Woods representation for the measured quadratures, but the Tomita-Takesaki theory tells us that there exists a separate, commuting representation and therefore the commutant will have a richer structure than encountered in the Fock vacuum case. We apply this to the question of quantum trajectories to the Davies-Fulling-Unruh model. Here, the two representations are interpreted as the fields in the right and left Rindler wedges. |
| title | Quantum Filtering at Finite Temperature |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2510.04967 |