Time-of-Flow Distributions in Discrete Quantum Systems: From Operational Protocols to Quantum Speed Limits

• URL: http://arxiv.org/abs/2504.09571v3
• Date: Fri, 01 Aug 2025 18:44:33 GMT
• Title: Time-of-Flow Distributions in Discrete Quantum Systems: From Operational Protocols to Quantum Speed Limits
• Authors: Mathieu Beau,
• Abstract summary: We propose a framework to quantify transition timing in discrete quantum systems via the time-of-flow (TF) distribution.<n>We apply this framework to optimize time-dependent Hamiltonians, analyze shortcut-to-adiabaticity protocols, and derive a transition-based quantum speed limit (TF-QSL) for both closed and open quantum systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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, 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.

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