Universal Properties of Critical Mixed States from Measurement and Feedback

• URL: http://arxiv.org/abs/2503.09597v1
• Date: Wed, 12 Mar 2025 17:58:55 GMT
• Title: Universal Properties of Critical Mixed States from Measurement and Feedback
• Authors: Zhehao Zhang, Yijian Zou, Timothy H. Hsieh, Sagar Vijay,
• Abstract summary: We explore the universal properties of mixed quantum matter obtained from "single-shot" adaptive evolution.<n>Mixed quantum states are characterized by altered long-distance correlations between local observables, mixed-state entropy, and entanglement negativity.
• Score: 1.0199622289463242
• License: http://creativecommons.org/licenses/by/4.0/
• 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 sub-leading, constant correction ($\gamma$), while the entanglement negativity can grow logarithmically with sub-region size, with a coefficient ($\alpha$); 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 ($i$) the critical point between a one-dimensional $Z_{2}\times Z_{2}$ symmetry-protected topological (SPT) order and a symmetry-broken state, and ($ii$) 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 $\alpha$ 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 $\alpha$ and $\gamma$ vary continuously with the strength of feedback. Numerical studies confirm these results.

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