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Detecting quantum many-body states with imperfect measuring devices

Kenan Uriostegui1,2, Chryssomalis Chryssomalakos3, Valentina Rascón Barajas3, Igor Vázquez Mota3, and Carlos Pineda1,4,*

  • *Contact author: carlospgmat03@gmail.com
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Phys. Rev. A 113, 042425 – Published 10 April, 2026

DOI: https://doi.org/10.1103/849f-3j77

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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Phys. Rev. A 113, 042425– Published 10 April, 2026
  • Received 16 December 2025
  • Accepted 16 March 2026
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