Pavel Kos

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We introduce the notion of the mixed state projected ensemble (MSPE), a collection of mixed states describing a local region of a quantum many-body system, conditioned upon incomplete measurements of the complementary region. This constitutes a generalization of the pure state projected ensemble in which measurements are assumed ideal and complete, and which has been shown to tend towards limiting pure state distributions depending only on symmetries of the system, thus representing a new kind of universality in quantum equilibration dubbed deep thermalization. We study the MSPE generated by solvable (1+1)d dual-unitary quantum circuit evolution, and identify the limiting mixed state distributions which emerge at late times depending on the size of the incomplete measurement, which we assume to be lossy, finding that they correspond to certain random density matrix ensembles known in the literature. We also derive the rate of the emergence of such universality. Furthermore, we uncover a sharp transition in the ensemble's capacity to teleport quantum information: the fidelity switches from zero to maximal when the number of lost measurement outcomes matches the number of teleported degrees of freedom. These results provide a framework for observing deep thermalization and sampling random matrix ensembles in realistic, lossy quantum simulators.
Based on PRL 135, 260402 (2025) (arXiv:2505.07795), done together with Xie-Hang Yu, Wen Wei Ho.

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University of Ljubljana
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Contact: Neil Dowling