利用齐雷尔森概率探测高斯态叠加的量子性

中文摘要 AI 辅助

高斯态的叠加态（包括圆态和广义圆态）展现出丰富的非经典特征，如维格纳负性和亚普朗克相空间结构。齐雷尔森概率是齐雷尔森进动协议的核心，其定义为：在等间隔时间测量进动正交分量时得到正结果的平均概率，经典边界为1/2 ± 1/(2d)。本工作计算了高斯态叠加的该概率：对于圆态（d个相干态的叠加），我们解析计算了其齐雷尔森概率，发现当d=3、5、7时违反经典边界；对于包含压缩的广义圆态，我们推导了一般表达式，并确定了可增强违反的参数区域。我们的结果为高斯态叠加的动力学非经典性提供了全面图谱，并确立其作为测试非经典性见证的通用平台。

英文摘要

Quantifying nonclassicality in continuous-variable systems remains a fundamental problem in quantum information science. The Tsirelson probability, central to the Tsirelson precession protocol, is defined as the average probability that a precessing quadrature yields a positive outcome when measured at $K$ equally spaced times, with the classical bound given by $1/2 \pm 1/(2K).$ In this work, we adopt this probability as a symmetry-sensitive probe to assess the quantumness of superpositions of Gaussian states in harmonic oscillators. We derive analytical constraints on Tsirelson probability arising from rotational and parity symmetries, and show that parity symmetry establishes a universal relation between the maximal and minimal Tsirelson probabilities within parity-related state families. Furthermore, we prove that even-fold rotational circular states cannot exhibit Tsirelson violation due to their definite parity. These results reveal how geometric symmetries of Gaussian-state superpositions determine their nonclassical behavior and provide a symmetry-based framework for probing quantumness in continuous-variable systems.

发表机构

• State Key Laboratory of Mathematical Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院数学科学重点实验室）
• School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）

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