Work

Non-Gaussianity of random quantum states

Year: 2026

Type: article

Abstract: We study the fermionic non-Gaussianity in typical quantum states, focusing on Haar random states of qubits with or without a global U (1) symmetry. Using the Weingarten calculus, we derive analytical predictions for the non-Gaussianity, defined as the relative entropy between the reduced density matrix and its Gaussianized counterpart. We identify two regimes controlled by the ratio between the subsystem and the system size, . For , the non-Gaussianity vanishes in the absence of symmetries, because typical reduced density matrices are exponentially close to the maximally mixed state. In the presence of a global U (1) symmetry, instead, it remains small but finite. By contrast, in the regime , the non-Gaussianity becomes extensive. These results establish the typical scaling of fermionic non-Gaussianity in random states and analyze how this is modified by the presence of global symmetries.

Source: Europhysics Letters (EPL)

DOI: 10.1209/0295-5075/ae9219

Authors: Filiberto Ares, Sara Murciano, Pasquale Calabrese

Institutions: Scuola Internazionale Superiore di Studi Avanzati, Istituto Nazionale di Fisica Nucleare, Université Paris-Saclay

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $1,895

Funder: European Research Council