基于有限能量GKP态的鲁棒CHSH自检测
Robust CHSH Self-Testing with Finite-Energy GKP States
AI总结：
本文通过全振子分析有限能量GKP态的CHSH测试，优化位移校准后提升了CHSH得分与贝尔对自检测的鲁棒性，为实验实现设备无关的贝尔对保证提供了理论支持。
AI中文摘要：
我们对有限能量GKP态的CHSH测试进行了全振子分析，该测试的观测得分可实现鲁棒贝尔对自检测。周期性分箱的位置和动量作为泡利测量设置，而光子数模4的固定二元粗粒化及其位移共轭则实现倾斜测量设置。对于经光子数滤波的GKP源，我们保留有限码字重叠，在所有光子数扇区上定义测量，且无需逻辑后校正即可计算物理关联。在规范理想逻辑位移\nd=√π\n下，CHSH值在每峰值压缩度超过4.56 dB时超过局域界限，Kaniewski的可提取性界限在超过5.02 dB时变得非平凡。仅使用独立表征的有限能量参数校准\nd\n，可将这些模型阈值分别降至4.21 dB和4.58 dB；在12 dB时，其将得分从2.69486提升至2.78858，对应目标态重叠界限从0.90758提升至0.97243。该校准在贝尔测试数据采集前固定。该位移激活奇数模4扇区，因此其固定先验赋值是真正的有限能量分量。该增益是确定性相位比特粗粒化特有的；用随机奇数扇区输出独立校准1比特POVM仅产生小得多的改进。这些是诚实模型的预测，而非损耗、探测效率或有限样本阈值。实验中，通过将观测CHSH得分的置信下界代入自检测定理，可对提取的贝尔对实现设备无关保证。
英文摘要：
We present a full-oscillator analysis of a finite-energy GKP CHSH test whose observed score yields robust Bell-pair self-testing. Periodically binned position and momentum give the Pauli settings, while a fixed binary coarse-graining of photon number modulo four and its displaced conjugate realize the tilted settings. For a number-filtered GKP source, we retain the finite codeword overlap, define the measurements on all photon-number sectors, and compute the physical correlations without logical post-corrections. With the canonical ideal-logical displacement \(d=\sqrtπ\), the CHSH value exceeds the local bound above \(4.56\) dB of per-peak squeezing, and Kaniewski's extractability bound becomes nontrivial above \(5.02\) dB. Calibrating only \(d\) using an independently characterized finite-energy parameter lowers these model thresholds to \(4.21\) dB and \(4.58\) dB, respectively; at \(12\) dB, it raises the score from \(2.69486\) to \(2.78858\) and the corresponding target-state overlap bound from \(0.90758\) to \(0.97243\). This calibration is fixed before Bell-test data are collected. The displacement activates the odd modulo-four sectors, so their fixed a priori assignments are a genuine finite-energy component. The large gain is specific to the deterministic phase-bit coarse-graining; independently calibrating the one-bit POVM with randomized odd-sector outcomes gives only a much smaller improvement. These are honest-model predictions, not loss, detection-efficiency, or finite-sample thresholds. In an experiment, a device-independent guarantee for an extracted Bell pair follows by inserting a confidence lower bound on the observed CHSH score into the self-testing theorem.
