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arXiv · 2512.08150

Detecting quantum many-body states with imperfect measuring devices

K. Uriostegui·C. Pineda·C. Chryssomalakos·V. Rascón Barajas·I. Vázquez Mota
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Abstract

We study a coarse-graining map arising from incomplete and imperfect addressing of particles in a multipartite quantum system. In its simplest form, corresponding to a two-qubit state, the resulting channel produces a convex mixture of the two partial traces. We derive the probability density of obtaining a given coarse-grained state, using geometric arguments for two qubits coarse-grained to one, and random-matrix methods for larger systems. As the number of qubits increases, the probability density sharply concentrates around the maximally mixed state, making nearly pure coarse-grained states increasingly unlikely. For two qubits, we also compute the inverse state needed to characterize the effective dynamics under coarse-graining and find that the average preimage of the maximally mixed state contains a finite singlet component. Finally, we validate the analytical predictions by inferring the underlying probabilities from Monte-Carlo-generated coarse-grained statistics.

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K. Uriostegui, C. Pineda, C. Chryssomalakos, V. Rascón Barajas, I. Vázquez Mota. 2025-12-09. Detecting quantum many-body states with imperfect measuring devices. https://doi.org/10.1103/849f-3j77

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