Context-Dependent Time-Energy Uncertainty Relations from Projective Quantum Measurements
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917079858282496 |
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| author | Beau, Mathieu |
| author_facet | Beau, Mathieu |
| contents | We introduce a general framework for defining context-dependent time distributions in quantum systems using projective measurements. The time-of-flow (TF) distribution, derived from population transfer rates into a measurement subspace, yields a time--energy uncertainty relation of the form $Δ\mathcal{T} \cdot ΔH \geq \hbar / (6\sqrt{3}) \cdot δθ$, where $δθ$ quantifies net population transfer. This bound applies to arbitrary projectors under unitary dynamics and reveals that time uncertainty is inherently measurement-dependent. We demonstrate the framework with two applications: a general time-of-arrival (TOA)-energy uncertainty relation and a driven three-level system under detuned coherent driving. The TF framework unifies timing observables across spin, atomic, and matter-wave systems, and offers an experimentally accessible route to probing quantum timing in controlled measurements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23059 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Context-Dependent Time-Energy Uncertainty Relations from Projective Quantum Measurements Beau, Mathieu Quantum Physics Mathematical Physics We introduce a general framework for defining context-dependent time distributions in quantum systems using projective measurements. The time-of-flow (TF) distribution, derived from population transfer rates into a measurement subspace, yields a time--energy uncertainty relation of the form $Δ\mathcal{T} \cdot ΔH \geq \hbar / (6\sqrt{3}) \cdot δθ$, where $δθ$ quantifies net population transfer. This bound applies to arbitrary projectors under unitary dynamics and reveals that time uncertainty is inherently measurement-dependent. We demonstrate the framework with two applications: a general time-of-arrival (TOA)-energy uncertainty relation and a driven three-level system under detuned coherent driving. The TF framework unifies timing observables across spin, atomic, and matter-wave systems, and offers an experimentally accessible route to probing quantum timing in controlled measurements. |
| title | Context-Dependent Time-Energy Uncertainty Relations from Projective Quantum Measurements |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2507.23059 |