无魔法的非稳定子性：经典可模拟量子电路无法区分的经典可模拟量子态
Testing nonstabilizerness only with stabilizer states
- School of Computational Sciences, Korea Institute for Advanced Study（韩国高等科学研究院计算科学学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文在魔法资源理论中构造了相互正交却无法被稳定子操作完美区分的稳定子态，提出“无魔法的非稳定子性”，并阐明其对量子数据隐藏、不可克隆和非克利福德门验证的意义。
AI中文摘要：
量子态区分在通过受限量子操作类别定义可能与不可能的操作方面发挥着核心作用。Bennett 等人的一项开创性结果 [Phys. Rev. A 59, 1070 (1999)] 证明，存在一组相互正交的可分量子态，无法通过局部操作和经典通信被完美区分，这一现象被称为无纠缠的非定域性。我们表明，在魔法资源理论中存在一种平行结构：存在一组相互正交的 stabilizer states（稳定子态），无法通过 stabilizer operations（稳定子操作）被完美区分；这些操作由 Clifford gates（克利福德门）、计算基测量以及附加的辅助稳定子态组成。我们将这一现象称为“无魔法的非稳定子性”，它揭示了经典高效可模拟稳定子态的制备与其区分之间的根本不对称性：后者无法由经典高效可模拟的量子电路完成。我们进一步讨论了这些发现对 quantum data hiding（量子数据隐藏）、稳定子态的不可克隆性，以及 non-Clifford gates（非克利福德门）的无条件验证的意义。
英文摘要：
The stabilizer formalism plays a central role in quantum information processing and quantum computing. Since stabilizer states and operations can be efficiently simulated classically and fault-tolerantly implemented in quantum error-correcting codes, quantum states and operations beyond the stabilizer framework, characterized by nonstabilizerness or magic, naturally emerge as resources for quantum computation. Here, we demonstrate that a quantum-information task involving only stabilizer states can reveal a fundamental limitation of stabilizer operations. Specifically, we construct a set of mutually orthogonal stabilizer states that cannot be perfectly distinguished using stabilizer operations and extend this construction to an arbitrary number of qubits. Our results provide an efficient test of nonstabilizerness without requiring the direct use of resourceful states or operations nor relying on computational-hardness assumptions. This nonstabilizerness test could serve as a resource-efficient benchmark for fault-tolerant quantum computers powered by magic-state injection, by providing quantitative bounds on the robustness of magic. More fundamentally, the resulting asymmetry between the preparation and discrimination of free states parallels "nonlocality without entanglement" in entanglement theory, revealing an unexpected connection between these two distinct quantum resource theories.
