Work

Asymptotically independent fluctuations of stabilizer Rényi entropy and entanglement in random unitary circuits

Year: 2025

Type: article

Abstract: We investigate numerically the joint distribution of magic (as described by the stabilizer 2-Rényi entropy M 2 ) and entanglement (as described by the von Neumann entropy S ) in N -qubit Haar-random quantum states. The distribution P N ( M 2 , S ) and the marginals become exponentially localized, and centered around the typical values, M 2 ̃ → N − 2 and S ̃ → N / 2 as N → ∞ . Magic and entanglement fluctuations are, however, found to become exponentially uncorrelated. While the set of stabilizer states grows exponentially with N , they nevertheless form a measure-zero subset of Haar-random states and thus occur with vanishing probability. Typical quantum states are characterized by large magic and entanglement entropy, and uncorrelated magic and entanglement fluctuations. The mutual information of the joint distribution vanishes exponentially as N → ∞ , implying that fluctuations of these two resources are not only uncorrelated but asymptotically independent.

Source: Physical Review Research

DOI: 10.1103/jplh-zl35

Authors: Dominik Szombathy, Angelo Valli, Cătălin Paşcu Moca, Lóránt Farkas, Gergely Zaránd

Institutions: Budapest University of Technology and Economics, University of Oradea

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,625