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This paper uses one measurement protocol with two different post-processing rules to define two distinct quantum time distributions, a flow-based one and an occupation-based one. Applied to tunneling through a rectangular barrier, they explain the Hartman effect in terms of early penetration, reflection, and spectrally filtered transmission. For quantum readers, the main point is foundational: "tunneling time" depends on which operational definition you choose, so the apparent saturation of delay is not a single physical quantity. The work is theoretical and has no direct application to quantum hardware or algorithms.
Complementary Quantum Time Distributions from a Single Operational Protocol
arXiv:2604.10339v3 Announce Type: replace Abstract: A single operational protocol based on free evolution and projective measurements yields inequivalent quantum time distributions through distinct post-processing procedures. We construct an activity-based time-of-flow (TF) distribution and a presence-based quantum stroboscopic (QS) distribution, providing complementary operational notions of time. Applied to tunneling through a rectangular barrier, the regional QS mean saturates as the barrier width increases, whereas the TF mean first decreases and eventually grows for larger widths. These contrasting behaviors provide an operational interpretation of the Hartman effect, the apparent saturation of tunneling delay with increasing barrier width, in terms of quantum time distributions associated with flow through the exit region and occupation within the barrier, capturing the roles of early penetration, dominant reflection, and spectrally filtered transmission.
Abstract:A single operational protocol based on free evolution and projective measurements yields inequivalent quantum time distributions through distinct post-processing procedures. We construct an activity-based time-of-flow (TF) distribution and a presence-based quantum stroboscopic (QS) distribution, providing complementary operational notions of time. Applied to tunneling through a rectangular barrier, the regional QS mean saturates as the barrier width increases, whereas the TF mean first decreases and eventually grows for larger widths. These contrasting behaviors provide an operational interpretation of the Hartman effect, the apparent saturation of tunneling delay with increasing barrier width, in terms of quantum time distributions associated with flow through the exit region and occupation within the barrier, capturing the roles of early penetration, dominant reflection, and spectrally filtered transmission.
arXiv:2604.10339 [quant-ph]
(or arXiv:2604.10339v3 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2604.10339 Focus to learn more arXiv-issued DOI via DataCite
Phys. Rev. A 114, L030201 (2026)
https://doi.org/10.1103/2h72-l3cn Focus to learn more DOI(s) linking to related resources
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