AI 中文总结
本文研究固定与自适应稳定器电路可实现测量下的最小误差量子态区分，推导单量子比特成功概率表达式及相关界，并将成果应用于量子随机存取码与酉合成保真度界。
AI 中文摘要
量子态区分任务为可区分性提供了操作性表征，在量子信息科学中具有核心作用。由于量子态区分的可实现成功概率既取决于待区分的量子态，也取决于允许的测量方式，因此在符合物理实际的测量约束下研究区分问题具有重要意义。本文研究了在固定稳定器电路和自适应稳定器电路均可实现的测量下的最小误差量子态区分问题。给定任意稳定器态辅助量子比特，我们证明固定稳定器电路不会提供额外的区分能力，而自适应电路则可以。接着，针对单量子比特系统，我们推导了在配备任意非稳定器辅助量子比特时两类电路的成功概率解析表达式，表明固定与自适应电路的性能差距依然存在。我们进一步考虑将非稳定器性直接融入测量算子的区分问题，将该优化问题表述为半定规划，并推导了插值量子比特稳定器极限与Helstrom极限的解析界。最后，我们阐述了该研究在量子随机存取码及有限魔法态下的酉合成保真度界中的应用。
英文摘要
The task of quantum state discrimination provides an operational characterization of distinguishability and plays a central role in quantum information science. Since the achievable success probability in quantum state discrimination depends both on the states being discriminated and on the allowed measurements, it is natural to study discrimination under physically motivated measurement constraints. Here, we investigate minimum-error quantum state discrimination under measurements implementable by both fixed and adaptive stabilizer circuits. Given arbitrary stabilizer-state ancillas, we show that fixed stabilizer circuits provide no additional discrimination power, whereas adaptive circuits do. Then, focusing on single-qubit systems, we derive analytical expressions for the success probability across both circuit classes when supplied with arbitrary (non-stabilizer) ancillas, showing that the performance gap between fixed and adaptive circuits persists. We further consider discrimination with non-stabilizerness incorporated directly into the measurement operators. Here, the optimization is formulated as a semidefinite program, and analytical bounds interpolating between the stabilizer and Helstrom limits for qubits are derived. Finally, we illustrate applications in quantum random access codes and bounds on unitary synthesis fidelity with a finite number of magic states.
Comments6 + 29 pages, 3 + 3 figures
