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  • Open Access

Universal Properties of Critical Mixed-States from Measurement and Feedback

Zhehao Zhang1,*, Yijian Zou2, Timothy H. Hsieh2, and Sagar Vijay1

  • *Contact author: zhehao@ucsb.edu
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PRX Quantum 6, 040363 – Published 15 December, 2025

DOI: https://doi.org/10.1103/66zv-8k1t

Abstract

We explore the universal properties of mixed quantum matter obtained from “single-shot” adaptive evolution, in which a quantum-critical ground-state is manipulated through a single round of local measurements and local unitary operations conditioned on spatially distant measurement outcomes. The resulting mixed quantum states are characterized by altered long-distance correlations between local observables, mixed-state entropy, and entanglement negativity. By invoking a coarse-grained, continuum description of single-shot adaptation in (1+1) dimensions, we find that the extensive mixed-state entropy exhibits a subleading, constant correction (γ), while the entanglement negativity can grow logarithmically with subregion size, with a coefficient (α); both constants can attain universal values which are distinct from the expected behavior in any quantum-critical ground-state. We investigate these properties in single-shot adaptation on (1) the critical point between a one-dimensional Z2×Z2 symmetry-protected topological (SPT) order and a symmetry-broken state, and (2) a spinful Tomonaga-Luttinger liquid. In the former case, adaptive evolution that decoheres one sublattice of the SPT can yield a critical mixed-state in which α attains a universal value, which is half of that in the original state. In the latter case, we show how adaptation—involving feedback on the spin degrees of freedom, after measuring the local charge—modifies long-distance correlations, and determine via an exact replica field-theoretic calculation that α and γ vary continuously with the strength of feedback. Numerical studies confirm these results.

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Popular Summary

In traditional many-body physics, quantum criticality describes the sharp, universal behavior that emerges when a material sits right at the brink of a phase transition, where systems with very different microscopic details share the same universal long-distance behavior. Today, controllable quantum simulators built from cold atoms, trapped ions, and superconducting qubits offer a rich toolbox—precise measurements and programmable unitary evolution—for exploring quantum criticality in a flexible and highly controlled way.

This work shows how these tools can turn measurements from a way to merely observe quantum systems into a resource for creating new universal states of matter. We start from a quantum system at criticality, perform a single round of local measurements, and then apply local unitary feedback conditioned on the measurement outcomes. The resulting state is mixed, yet it retains universal, critical quantum correlations and long-range entanglement. We develop a general framework to describe these critical mixed-states and identify universal constants that govern their entanglement, independent of microscopic details. In concrete examples of interacting spinful fermions, these constants can be tuned continuously using feedback.

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PRX Quantum 6, 040363– Published 15 December, 2025
  • Received 23 April 2025
  • Revised 22 August 2025
  • Accepted 10 November 2025
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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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