Work

Rényi Multi-entropy for Stabilizer States: A Finite Field Gauss Sum Problem

Year: 2026

Type: preprint

Abstract: Rényi multi-entropy probes multi-partite structure beyond bipartite spectra, but its behavior in general quantum states and the entanglement structure it captures remain poorly understood. We develop a finite field Gauss sum framework for calculating it in stabilizer states. Within this framework, the replica contraction reduces to a quadratic Gauss sum if and only if the state is locally unitarily equivalent to a stabilizer state. We obtain analytic expressions for the Rényi multi-entropy of all tree graph states and large families of loop graph states. In contrast to their flat bipartite Rényi spectra, stabilizer states generically have nonflat Rényi multi-entropy spectra.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.26814

Authors: Czech, Bartlomiej, Feng, Yichen, Harper, Jonathan, Ju, Xin-Xiang, Zhao, Yang

Institutions: Tsinghua University, Case Western Reserve University, University of Chinese Academy of Sciences, Kyoto University, Yukawa Institute for Theoretical Physics

Language: English

Topic: Quantum Information and Cryptography

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Aspen Center for Physics, Ministry of Education, Culture, Sports, Science and Technology, National Natural Science Foundation of China, Tsinghua University, Japan Society for the Promotion of Science

Awards: G1105538003, G1418984100, G8255059130

OpenAlex ID: W7223036678

Cites: 29

Cited by: 3

Related to: 10