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arXiv · 2501.11489

Independent stabilizer R\'enyi entropy and entanglement fluctuations in random unitary circuits

Dominik Szombathy·Angelo Valli·Cătălin Paşcu Moca·Lóránt Farkas·Gergely Zaránd
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Abstract

We investigate numerically the joint distribution of magic ($M$) and entanglement ($S$) in $N$-qubit Haar-random quantum states. The distribution $P_N(M,S)$ as well as the marginals become exponentially localized, and centered around the values $\tilde{M_2} \to N-2$ and $\tilde{S} \to N/2$ as $N\to\infty$. Magic and entanglement fluctuations are, however, found to become exponentially uncorrelated. Although exponentially many states with magic $M_2=0$ and entropy $S\approx S_\text{Haar}$ exist, they represent an exponentially small fraction compared to typical quantum states, which are characterized by large magic and entanglement entropy, and uncorrelated magic and entanglement fluctuations.

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Dominik Szombathy, Angelo Valli, Cătălin Paşcu Moca, Lóránt Farkas, Gergely Zaránd. 2025-01-20. Independent stabilizer R\'enyi entropy and entanglement fluctuations in random unitary circuits. https://doi.org/10.1103/jplh-zl35

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