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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2504.09571 |
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| _version_ | 1866918147706060800 |
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| author | Beau, Mathieu |
| author_facet | Beau, Mathieu |
| contents | We propose a general and experimentally accessible framework to quantify transition timing in discrete quantum systems via the time-of-flow (TF) distribution. Defined from the rate of population change in a target state, the TF distribution can be reconstructed through repeated projective measurements at discrete times on independently prepared systems, thus avoiding Zeno inhibition. In monotonic regimes, it admits a clear interpretation as a time-of-arrival (TOA) or time-of-departure (TOD) distribution. We apply this approach to optimize time-dependent Hamiltonians, analyze shortcut-to-adiabaticity (STA) protocols, study non-adiabatic features in the dynamics of a three-level time-dependent detuning model, and derive a transition-based quantum speed limit (TF-QSL) for both closed and open quantum systems. We also establish a lower bound on temporal uncertainty and examine decoherence effects, demonstrating the versatility of the TF framework for quantum control and diagnostics. This method provides both a conceptual tool and an experimental protocol for probing and engineering quantum dynamics in discrete-state platforms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09571 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time-of-Flow Distributions in Discrete Quantum Systems: From Operational Protocols to Quantum Speed Limits Beau, Mathieu Quantum Physics Mathematical Physics We propose a general and experimentally accessible framework to quantify transition timing in discrete quantum systems via the time-of-flow (TF) distribution. Defined from the rate of population change in a target state, the TF distribution can be reconstructed through repeated projective measurements at discrete times on independently prepared systems, thus avoiding Zeno inhibition. In monotonic regimes, it admits a clear interpretation as a time-of-arrival (TOA) or time-of-departure (TOD) distribution. We apply this approach to optimize time-dependent Hamiltonians, analyze shortcut-to-adiabaticity (STA) protocols, study non-adiabatic features in the dynamics of a three-level time-dependent detuning model, and derive a transition-based quantum speed limit (TF-QSL) for both closed and open quantum systems. We also establish a lower bound on temporal uncertainty and examine decoherence effects, demonstrating the versatility of the TF framework for quantum control and diagnostics. This method provides both a conceptual tool and an experimental protocol for probing and engineering quantum dynamics in discrete-state platforms. |
| title | Time-of-Flow Distributions in Discrete Quantum Systems: From Operational Protocols to Quantum Speed Limits |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2504.09571 |