Complexity of quantum states in the stabilizer formalism

• URL: http://arxiv.org/abs/2604.20118v1
• Date: Wed, 22 Apr 2026 02:29:12 GMT
• Title: Complexity of quantum states in the stabilizer formalism
• Abstract summary: We propose an information-theoretic quantifier for the complexity of quantum states within the stabilizer formalism of quantumvariable.<n>We establish the fundamental properties of this quantifier and demonstrate that state complexity is closely related to the nonstabilizerness of quantum states.
• Score: 6.315323176162257
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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