Resolving the phase space

Zdenek Hradil; Jaroslav Rehacek

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arXiv · 2605.29784

Resolving the phase space

Zdenek Hradil·Jaroslav Rehacek

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Abstract

We show that the effective resolution of quantum inference is determined by a sampling Gram operator that defines the experimentally accessible degrees of freedom and the reconstruction bandwidth supported by the data. Acting analogously to a transfer function in classical imaging, this operator together with scaling of deviance provides an operational criterion for distinguishing genuinely resolved features from structures arising from incomplete sampling, statistical fluctuations, or reconstruction assumptions. Reconstruction in the Gram eigenbasis emerges naturally as a measurement-adapted compression of the inference problem, retaining only those modes supported by typical measurement outcomes. Within finite frame theory, the same structure appears as the frame operator governing stable reconstruction. The resulting framework connects quantum tomography, inverse reconstruction, and measurement resolution, providing a practical tool for assessing whether fine phase-space structures inferred in contemporary experiments are genuinely resolved by the measurement or merely reconstructed by the model.

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Zdenek Hradil, Jaroslav Rehacek. 2026-07-31. Resolving the phase space. https://arxiv.org/abs/2605.29784

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