高斯玻色采样中的反聚束与纠缠
Anticoncentration and entanglement in Gaussian boson sampling
- Joint Quantum Institute, Department of Physics, NIST/University of Maryland（联合量子研究所，物理系，美国国家标准与技术研究院/马里兰大学）
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（量子信息与计算科学联合中心，美国国家标准与技术研究院/马里兰大学）
- Microsoft Quantum（微软量子）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文针对高斯玻色采样的反聚束与纠缠，推导对称高斯乘积 hafnians 二阶矩、Rényi-α Page 曲线的闭式表达式，研究不等输入压缩参数下 Rényi-2 熵 Page 曲线的性质，扩展了等压缩相关结果。
AI中文摘要：
反聚束与纠缠是用于研究不同 regime 下高斯玻色采样经典难易程度的两个性质。本文围绕高斯玻色采样中的反聚束与纠缠考虑三个方向：(1) 推导对称高斯乘积的 hafnians 的二阶矩闭式表达式，利用该式可根据压缩输入模式的数量精确确定反聚束转变；(2) 推导高斯玻色采样的 Rényi-α Page 曲线闭式表达式；(3) 研究不等输入压缩参数 $(s_i)_i$，证明平均情况 Rényi-2 熵 Page 曲线关于幅值 $|s_i|$ 的估计值及单调性，这可将等压缩结果扩展至不等压缩场景。
英文摘要：
Anticoncentration and entanglement are two properties used to study classical hardness or easiness of Gaussian boson sampling in varying regimes. In this paper, we consider three directions concerning anticoncentration and entanglement in Gaussian boson sampling: (1) We derive closed-form expressions for the second moment of hafnians of symmetric Gaussian products, and use this to precisely locate the anticoncentration transition as a function of the number of squeezed input modes. (2) We derive closed-form expressions for the Rényi-$α$ Page curves for Gaussian boson sampling. (3) We study unequal input squeezing parameters $(s_i)_i$, and prove estimates as well as monotonicity of the average-case Rényi-2 entropy Page curve in terms of the magnitudes $|s_i|$, which allow for extending equal squeezing results to unequal squeezing.
