玻色子量子熵功率不等式中的等式条件
Equality in the Bosonic Quantum Entropy Power Inequality
- School of Mathematics and Statistics Xi’an Jiaotong University（西安交通大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究确定了玻色子量子熵功率不等式在有限平均光子数独立输入下的完整等式类，证明等式成立当且仅当输入为具有相同协方差矩阵的高斯态，并允许任意位移。
AI中文摘要：
玻色子量子熵功率不等式以输入熵为界约束分束器输出的熵。我们确定了在有限平均光子数的独立输入下其完整的等式类：对于任意数量的模式和任意严格介于零和一之间的透射率，在线性或指数形式下等式成立当且仅当输入为具有相同协方差矩阵的高斯态，允许任意位移。主要步骤表明，一个输出的等式成立迫使两个输出独立：一个热辅助将等式转化为固定噪声信道下互信息的保持，而一个双结果仪器表明互信息的保持要求与参考态形成乘积态。量子Darmois-Skitovich定理随后给出高斯性，而中心极限论证将指数等式简化为线性等式。
英文摘要：
The bosonic quantum entropy power inequality bounds the entropy of a beam-splitter output in terms of the input entropies. We determine its complete equality class among independent inputs of finite mean photon number: for any number of modes and any transmissivity strictly between zero and one, equality in either the linear or the exponential form holds if and only if the inputs are Gaussian with the same covariance matrix, allowing arbitrary displacements. The main step shows that equality for one output forces the two outputs to be independent: a thermal auxiliary converts equality into preservation of mutual information by a fixed noisy channel, and a two-outcome instrument shows that preservation of mutual information requires a product state with the reference. The quantum Darmois--Skitovich theorem then gives Gaussianity, while a central-limit argument reduces exponential equality to linear equality.
