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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.11489 |
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| _version_ | 1866918312159477760 |
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| author | Szombathy, Dominik Valli, Angelo Moca, Cătălin Paşcu Farkas, Lóránt Zaránd, Gergely |
| author_facet | Szombathy, Dominik Valli, Angelo Moca, Cătălin Paşcu Farkas, Lóránt Zaránd, Gergely |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11489 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Independent stabilizer Rényi entropy and entanglement fluctuations in random unitary circuits Szombathy, Dominik Valli, Angelo Moca, Cătălin Paşcu Farkas, Lóránt Zaránd, Gergely Quantum Physics 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. |
| title | Independent stabilizer Rényi entropy and entanglement fluctuations in random unitary circuits |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2501.11489 |