Complexity of quantum states in the stabilizer formalism
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913053800398848 |
|---|---|
| author | Fu, Shuangshuang Luo, Shunlong Zhang, Yue |
| author_facet | Fu, Shuangshuang Luo, Shunlong Zhang, Yue |
| contents | We initiate an investigation into a notion of state complexity for discrete-variable quantum systems. Specifically, we propose an information-theoretic quantifier for the complexity of quantum states within the stabilizer formalism of quantum computation. This is achieved by leveraging the symmetric Jordan product (associated with classicality) and the skew-symmetric Lie product (linked to quantumness) between the square root of the quantum state and the Heisenberg-Weyl displacement operators. We establish the fundamental properties of this quantifier and demonstrate that state complexity is closely related to the nonstabilizerness of quantum states via the $L^4$-norm of their characteristic functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20118 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Complexity of quantum states in the stabilizer formalism Fu, Shuangshuang Luo, Shunlong Zhang, Yue Quantum Physics We initiate an investigation into a notion of state complexity for discrete-variable quantum systems. Specifically, we propose an information-theoretic quantifier for the complexity of quantum states within the stabilizer formalism of quantum computation. This is achieved by leveraging the symmetric Jordan product (associated with classicality) and the skew-symmetric Lie product (linked to quantumness) between the square root of the quantum state and the Heisenberg-Weyl displacement operators. We establish the fundamental properties of this quantifier and demonstrate that state complexity is closely related to the nonstabilizerness of quantum states via the $L^4$-norm of their characteristic functions. |
| title | Complexity of quantum states in the stabilizer formalism |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2604.20118 |