Gauge freedoms in unravelled quantum dynamics: When do different continuous measurements yield identical quantum trajectories?
Quantum trajectories of a Markovian open quantum system arise from the back-action of measurements performed in the environment with which the system interacts. In this work, we consider counting measurements of quantum jumps, corresponding to different representations of the same quantum master equ...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-07-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-07-09-1787/pdf/ |
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| author | Calum A. Brown Katarzyna Macieszczak Robert L. Jack |
| author_facet | Calum A. Brown Katarzyna Macieszczak Robert L. Jack |
| author_sort | Calum A. Brown |
| collection | DOAJ |
| description | Quantum trajectories of a Markovian open quantum system arise from the back-action of measurements performed in the environment with which the system interacts. In this work, we consider counting measurements of quantum jumps, corresponding to different representations of the same quantum master equation. We derive necessary and sufficient conditions under which these different measurements give rise to the same unravelled quantum master equation, which governs the dynamics of the probability distribution over pure conditional states of the system. Since that equation uniquely determines the stochastic dynamics of a conditional state, we also obtain necessary and sufficient conditions under which different measurements result in identical quantum trajectories. We then consider the joint stochastic dynamics for the conditional state and the measurement record. We formulate this in terms of labelled quantum trajectories, and derive necessary and sufficient conditions under which different representations lead to equivalent labelled quantum trajectories, up to permutations of labels. As those conditions are generally stricter, we finish by constructing coarse-grained measurement records, such that equivalence of the corresponding partially-labelled trajectories is guaranteed by equivalence of the trajectories alone. These general results are illustrated by two examples that demonstrate permutation of labels, and equivalence of different quantum trajectories. |
| format | Article |
| id | doaj-art-5f8726dd3b204ee1a5ec2b3f169005ef |
| institution | DOAJ |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-5f8726dd3b204ee1a5ec2b3f169005ef2025-08-20T02:40:14ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-07-019178710.22331/q-2025-07-09-178710.22331/q-2025-07-09-1787Gauge freedoms in unravelled quantum dynamics: When do different continuous measurements yield identical quantum trajectories?Calum A. BrownKatarzyna MacieszczakRobert L. JackQuantum trajectories of a Markovian open quantum system arise from the back-action of measurements performed in the environment with which the system interacts. In this work, we consider counting measurements of quantum jumps, corresponding to different representations of the same quantum master equation. We derive necessary and sufficient conditions under which these different measurements give rise to the same unravelled quantum master equation, which governs the dynamics of the probability distribution over pure conditional states of the system. Since that equation uniquely determines the stochastic dynamics of a conditional state, we also obtain necessary and sufficient conditions under which different measurements result in identical quantum trajectories. We then consider the joint stochastic dynamics for the conditional state and the measurement record. We formulate this in terms of labelled quantum trajectories, and derive necessary and sufficient conditions under which different representations lead to equivalent labelled quantum trajectories, up to permutations of labels. As those conditions are generally stricter, we finish by constructing coarse-grained measurement records, such that equivalence of the corresponding partially-labelled trajectories is guaranteed by equivalence of the trajectories alone. These general results are illustrated by two examples that demonstrate permutation of labels, and equivalence of different quantum trajectories.https://quantum-journal.org/papers/q-2025-07-09-1787/pdf/ |
| spellingShingle | Calum A. Brown Katarzyna Macieszczak Robert L. Jack Gauge freedoms in unravelled quantum dynamics: When do different continuous measurements yield identical quantum trajectories? Quantum |
| title | Gauge freedoms in unravelled quantum dynamics: When do different continuous measurements yield identical quantum trajectories? |
| title_full | Gauge freedoms in unravelled quantum dynamics: When do different continuous measurements yield identical quantum trajectories? |
| title_fullStr | Gauge freedoms in unravelled quantum dynamics: When do different continuous measurements yield identical quantum trajectories? |
| title_full_unstemmed | Gauge freedoms in unravelled quantum dynamics: When do different continuous measurements yield identical quantum trajectories? |
| title_short | Gauge freedoms in unravelled quantum dynamics: When do different continuous measurements yield identical quantum trajectories? |
| title_sort | gauge freedoms in unravelled quantum dynamics when do different continuous measurements yield identical quantum trajectories |
| url | https://quantum-journal.org/papers/q-2025-07-09-1787/pdf/ |
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