【作者】 张昆；

【导师】 荆杰泰；

【作者基本信息】 华东师范大学 ， 光学， 2022， 博士

【摘要】 量子态是量子信息的必备要素,它的非经典性是实现量子优越性的重要保证。近年,在连续变量光量子信息领域中,由于多模系统能提供更多的量子资源,非高斯系统比纯粹的高斯系统更具优势,光量子态的研究已呈现从双模纠缠到多模纠缠,从高斯到非高斯的趋势。探索非高斯态的非经典性及其量子优越性成为当前研究热点。目前,减光子操作制备的多模非高斯态,其纠缠内在不可分性、多模Wigner负性、非高斯性局域扩散性等特性已被发现,但探索更多非经典性并挖掘其潜在应用价值仍十分重要。本文将研究该多模非高斯态的非经典性及其应用。主要内容包括:1.证明高斯态在减光子操作下,其两体纠缠度的最大增量为ln(2)。众所周知,减光子操作可增加高斯态的纠缠度,但具体增量尚不明确。我们基于Rényi-2熵的纠缠度量,证明高斯态在减光子操作后,两体纠缠度的增量极限为ln(2)。这个上限对所有高斯态都有效,与高斯态的模式数量和纯度无关。该结论为多模高斯态纠缠蒸馏的实现提供了理论依据。2.发现减光子操作可提升部分高斯态的纯度,并证明其最大增量为20%。由于不可避免的耗散和退相干效应,实验上无法获得纯态,如何提升量子态的纯度变得迫在眉睫。我们发现可直接利用减光子操作提高部分高斯态的纯度,并证明纯度的最大增量为20%。在此基础上,我们分析了单模和双模高斯态纯化的案例,验证了以上结论。该方案为多模高斯态纯化的实验实现提供了理论依据。3.发现可利用相敏非高斯性优化相位灵敏度。利用量子算符的对易性和Bogoliubov变换,找到一种新型的灵敏度增强机制——利用相敏非高斯性优化相位灵敏度。以减光子操作的SU(1,1)干涉仪为例,我们不仅发现该机制能极大增强相位灵敏度,而且给出其适用范围——弱光环境下的小相位测量。该机制是利用非经典性实现量子优越性的一个成功案例。我们不仅发现了减光子操作制备的非高斯态的更多非经典性及其特性,而且挖掘了其应用价值。这些研究结果将助推多模非高斯量子网络的实验实现与连续变量光量子信息的理论发展。更多还原

【Abstract】 The non-classicality of quantum states is an important guarantee to realize the quantum superiority of quantum information.Due to multimode systems can provide more quantum resources and non-Gaussian systems have more advantages than pure Gaussian systems,the study of optical quantum states has shown a trend from two-mode entanglement to multimode entanglement,and from Gaussian to non-Gaussian.In the field of continuous variable quantum information,it has become a hot research topic to explore the non-classicality and its quantum superiority of non-Gaussian states.For the multimode nonGaussian states prepared by single photon subtraction operation,the intrinsic indivisibility of entanglement,the multimode Wigner negative,the local diffusion of non-Gaussianity and other properties have been found recently.However,it is still important to explore more non-classicality and tap their potential application value.In this paper,we will study the non-classicality and its application of this kind of multimode non-Gaussian states.The main contents include:1.It is proved that the maximum increment of two-body entanglement of Gaussian state is ln(2)under single-photon subtraction operation.It is well known that photon subtraction can increase the entanglement degree of Gaussian states,but the specific increment is not clear.Based on the entanglement measure of Renyi-2 entropy,we show that the incremental limit of two-body entanglement for Gaussian states after the single-photon subtraction operation is ln(2).This upper bound is valid for all Gaussian states,regardless of the number of modes and purity of the Gaussian state.This conclusion provides a theoretical basis for the realization of multi-mode Gaussian state entanglement distillation.2.It is found that the single photon subtraction operation can improve the purity of some Gaussian states,and the maximum increment is 20%.Due to the inevitable dissipation and decoherence effects,pure states cannot be obtained experimentally.How to improve the purity of quantum states becomes imminent.We find that the purity of some Gaussian states can be improved directly by using the single photon subtraction operation,and prove that the maximum increment of purity is 20%.On this basis,we analyze the case of single-mode and dual-mode Gaussian state purification, and verify the above conclusions.This scheme provides a theoretical basis for the experimental realization of multimode Gaussian state purification.3.It is found that phase sensitivity can be optimized by phase sensitive non-Gaussianity.By using the commutation of quantum operators and the Bogoliubov transform,a new sensitivity enhancement mechanism is found, which uses phase-sensitive non-Gaussianity to optimize the phase sensitiv-ity.Taking the SU(1,1)interferometer operated by photon subtraction as an example,we find that this mechanism can greatly enhance the phase sensitivity,and give its application scope——small phase measurement in weak light environment.This mechanism is a successful case of realizing quantum superiority by using non-classicality.We not only find more non-classicality of non-Gaussian states prepared by photon subtraction operation,but also explore their application value.These results will boost the experimental realization of multimode non-Gaussian quantum networks and the theoretical development of continuous variable optical quantum information.更多还原