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  • Open Access

Randomly Monitored Quantum Codes

Dongjin Lee1,2,* and Beni Yoshida1,†

  • *Contact author: dlee@perimeterinstitute.ca
  • †Contact author: byoshida@perimeterinstitute.ca
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PRX Quantum 7, 020352 – Published 5 June, 2026

DOI: https://doi.org/10.1103/6s65-ylvw

Abstract

Recent studies of monitored quantum dynamics have revealed that projective measurements, traditionally viewed as decohering operations, can instead generate and sustain long-range entanglement. Motivated by these, we ask how many physical qubits must be measured in random basis to irreversibly destroy quantum information encoded in a quantum error-correcting code. We study this problem for a broad class of stabilizer and subsystem codes, derive necessary and sufficient conditions for measurement-induced information destruction, and show that many codes, including concatenated and topological codes, achieve the maximal measurement threshold pmth=1, meaning that the encoded information survives as long as arbitrarily small but finite fraction of physical qubits remain unmeasured. Beyond this surprising robustness, we find a structural relation underlying maximal thresholds. Namely, we prove that if the Pauli basis of the logical operator measured at full measurement does not concentrate on a single Pauli, then the measurement threshold always satisfies pmth=1. This result uncovers a structural relation between logical measurement statistics and stability under partial measurement, revealing a general mechanism by which access to measurement outcomes enhances decodability under monitored dynamics.

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Popular Summary

Quantum measurements have long been regarded as destroying quantum information. Does this belief hold even when that information is protected in quantum error-correcting codes? We found that a broad class of quantum error-correcting codes, including the leading designs used in quantum computing research, is remarkably robust against local random measurements. In fact, the encoded information can survive even when nearly every physical qubit has been randomly measured. We explain this phenomenon by proving a general structural relation between the maximum measurement threshold and the measurement statistics of the logical operator. Our work suggests that, even after random measurements, a modest degree of quantum encoding can enable a system to retain memory of its initial state, opening a new perspective on their role in quantum information processing.

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PRX Quantum 7, 020352– Published 5 June, 2026
  • Received 7 June 2024
  • Revised 23 October 2025
  • Accepted 16 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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