648 Hilbert-space dimensionality in a biphoton frequency comb: entanglement of formation and Schmidt mode decomposition
648 Hilbert-space dimensionality in a biphoton frequency comb: entanglement of formation and Schmidt mode decomposition
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DOI：
10.1038/s41534-021-00388-0
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发表时间：
2021-03-11
影响因子：
7.6
通讯作者：
Wong, Chee Wei
中科院分区：
文献类型：
--
作者：
Chang, Kai-Chi;Cheng, Xiang;Wong, Chee Wei
QUDIT纠缠是用于量子信息处理的必不可少的资源，因为增加维度为量子通信中的更高容量和增加的噪声弹性提供了途径，以及群集状态量子量子计算。在连续变化的时频纠缠中，每个光子编码多个量子位仅受频率相关带宽和检测正时抖动的限制。在这里，我们专注于双光子频率梳子（BFC）中的离散可变时频纠缠，通过用45.32 GHz游离磁带范围（FSR）和1.56 GHz进行过滤信号和怠速输出来生成。来自连续波（CW）的II型自发参数下调（SPDC）的全宽度最大最大（FWHM）。我们生成了一个BFC，其时间限制/频率为希尔伯特空间维度至少为324，基于纯状态的假设。这种BFC的维度与其后启动的极化纠缠相结合后，高达648，表明潜在的6.28位/光子经典信息能力。 BFC表现出反复出现的Hong-Ou-Mandel（HOM）在61个时间垃圾箱中倾斜，最大可见性为98.4％，没有意外重合的校正。在选择后的测量中，它违反了clauser-horne-horne-holt-holt（CHSH）的不平等，极化纠缠的不平等范围高达18.5标准偏差，S参数为2.771。它具有16个时箱中的弗兰森干扰复发，最大可见性为96.1％，没有意外巧合的校正。从零体到三阶弗朗森干扰，我们推断出形成（E-）的纠缠（e-os）高达1.89 +/- 0.03 ebits-where 2 ebit是4 x 4尺寸的biphoton的最大纠缠 - 较低绑在61个时态BFC的高维纠缠上。为了进一步表征付费/频率的BFC，我们获得了使用具有45.32、15.15和5.03 GHz FSR的腔产生的BFC的Schmidt模式分解。这些分解确认了傅立叶转变二元性的时频缩放。此外，我们介绍了共轭弗兰森干涉法理论，因为它的特征是国家的联合时间强度（JTI），这可以进一步有助于区分纯状态BFC和混合状态纠缠频率对，尽管实验实现具有挑战性并且尚未可用。总之，我们的BFC是高维量子信息处理和高维量子密钥分布（QKD）的平台。
Qudit entanglement is an indispensable resource for quantum information processing since increasing dimensionality provides a pathway to higher capacity and increased noise resilience in quantum communications, and cluster-state quantum computations. In continuous-variable time-frequency entanglement, encoding multiple qubits per photon is only limited by the frequency correlation bandwidth and detection timing jitter. Here, we focus on the discrete-variable time-frequency entanglement in a biphoton frequency comb (BFC), generating by filtering the signal and idler outputs with a fiber Fabry-Perot cavity with 45.32 GHz free-spectral range (FSR) and 1.56 GHz full-width-at-half-maximum (FWHM) from a continuous-wave (cw)-pumped type-II spontaneous parametric downconverter (SPDC). We generate a BFC whose time-binned/frequency-binned Hilbert space dimensionality is at least 324, based on the assumption of a pure state. Such BFC's dimensionality doubles up to 648, after combining with its post-selected polarization entanglement, indicating a potential 6.28 bits/photon classical-information capacity. The BFC exhibits recurring Hong-Ou-Mandel (HOM) dips over 61 time bins with a maximum visibility of 98.4% without correction for accidental coincidences. In a post-selected measurement, it violates the Clauser-Horne-Shimony-Holt (CHSH) inequality for polarization entanglement by up to 18.5 standard deviations with an S-parameter of up to 2.771. It has Franson interference recurrences in 16 time bins with a maximum visibility of 96.1% without correction for accidental coincidences. From the zeroth- to the third-order Franson interference, we infer an entanglement of formation (E-of) up to 1.89 +/- 0.03 ebits-where 2 ebits is the maximal entanglement for a 4 x 4 dimensional biphoton-as a lower bound on the 61 time-bin BFC's high-dimensional entanglement. To further characterize time-binned/frequency-binned BFCs we obtain Schmidt mode decompositions of BFCs generated using cavities with 45.32, 15.15, and 5.03 GHz FSRs. These decompositions confirm the time-frequency scaling from Fourier-transform duality. Moreover, we present the theory of conjugate Franson interferometry-because it is characterized by the state's joint-temporal intensity (JTI)-which can further help to distinguish between pure-state BFC and mixed state entangled frequency pairs, although the experimental implementation is challenging and not yet available. In summary, our BFC serves as a platform for high-dimensional quantum information processing and high-dimensional quantum key distribution (QKD).