Multimode cat-state entanglement and network teleportation
Ba An Nguyen, Jaewan Kim
提出了多模纠缠猫态的产生方案和网络隐形传态协议。对于对称和非对称网络，推导出了成功隐形传态的概率的显式表达式。
Schemes for generation and protocols for network teleportation of multimode entangled cat-states are proposed. Explicit expressions for probability of successful teleportation are derived for both symmetric and asymmetric networks.
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We develop a simple and efficient theoretical model to understand the quantum properties of broadband continuous variable quantum teleportation. We show that, if stated properly, the problem of multimode teleportation can be simplified to teleportation of a single effective mode that describes the input state temporal characteristic. Using that model, we show how the finite bandwidth of squeezing and external noise in the classical channel affect the output teleported quantum field. We choose an approach that is especially relevant for the case of non-Gaussian non-classical quantum states and …
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Quantum Holographic Teleportation of Light Fields
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Teleportation plays an important role in the communication of quantum information between the nodes of a quantum network and is viewed as an essential ingredient for long-distance Quantum Cryptography. We describe a method to teleport the quantum information carried by a photon in a superposition of a number $d$ of light modes (a "qudit") by the help of $d$ additional photons based on transcription. A qudit encoded into a single excitation of $d$ light modes (in our case Laguerre-Gauss modes which carry orbital angular momentum) is transcribed to $d$ single-rail photonic qubits, which are spat…
Quantum repeater via entangled phase modulated multimode coherent states
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Entanglement of pair cat states and teleportation
利用纠缠的相对熵研究了相位阻尼信道中猫对态的纠缠。结果表明，在相位阻尼通道中，猫对态总是可分离的。此外，我们还利用光子数和和相位差的联合测量分析了对猫态隐形传态的保真度。
Broadband teleportation
研究了未知宽带电磁场的量子隐形传态。连续变量隐形传态协议由Braunstein和Kimble [Phys. Rev. { \bf 80}，869（1998）]中提出的用于传送电磁场单模量子态的方法推广到有限带宽多模场的情况。我们讨论了具有不同输入态的连续变量隐形传态的判据，并将其应用于宽带光场的隐形传态。我们首先考虑作为一组输入场（一个独立的状态捕获器从其中提取要传送的输入）具有未知相干振幅的任意纯高斯态（压缩态或相干态）。这组输入态进一步限制为相干态的字母表，Furusawa { \it et al.}在实验中使用了这组输入态。[Science { \bf 282}，706（1998）]。它需要单位增益的隐形传态来优化隐形传态的保真度。在我们的宽带方案中，由于压缩态纠缠的有限程度，通过单位增益隐形传态增加的多余噪声仅仅是（纠缠）源的压缩谱的两倍，因为它的“安静正交”。"半个纠缠态（双模压缩真空态）的隐形传态，即，在一定的非单位增益条件下，对“纠缠交换”及其验证进行了优化.我们还将基于van Loock和Braunstein的单模方案[Phys.Rev.A { \bf 61}，10302（2000）]给出这种连续变量纠缠交换的宽带描述。
Barut-Girardello coherent states for sp(N,C) and multimode Schrödinger cat states
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Entanglement Teleportation Through Cat-like States
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In continuous-variable quantum information, non-Gaussian entangled states that are obtained from Gaussian entangled states via photon subtraction are known to contain more entanglement. This makes them better resources for quantum information processing protocols, such as, quantum teleportation. We discuss the teleportation of non-Gaussian, non-classical Schrödinger-cat states of light using two-mode squeezed vacuum light that is made non-Gaussian via subtraction of a photon from each of the two modes. We consider the experimentally realizable cat states produced by subtracting a photon from t…
I theoretically investigate how the entanglement properties of a two-mode squeezed vacuum state (TMSVS) can be enhanced by operating quantum-optical catalysis on each mode of the TMSVS. The quantum-optical catalysis is simply mixing one photon at the beam splitter and post-select the beam-splitter (BS) output based on detection of one photon, first proposed by Lvovsky and Mlynek [Phys. Rev. Lett. 88, 250401 (2002)]. I find that there exists some enhancement in the entanglement properties (namely, entanglement entropy, second-order Einstein-Podolsky-Rosen correlation, and the fidelity of quantu…
Stochastic phase-space simulation of multimode cat states via the positive-P representation
本文提出利用正P相空间方法模拟多模式猫态的暂态动力学，克服了传统方法在大规模系统中的限制，展示了该方法在处理非高斯态模拟中的有效性。
Quantum teleportation of cat states with binary-outcome measurements
针对标准连续变量隐形传态在部分平台不适用的问题，提出基于分束器操作和二元结果测量的猫态量子隐形传态协议，适用于多种平台，多次测量可获近完美保真度并讨论了最优参数。
The Schrödinger's-cat state is created from the macroscopic superposition of coherent states and is well-known to be a useful resource for quantum information processing protocols. In order to extend such protocols to a global scale, we study the continuous variable (CV) teleportation of the cat state via a satellite in low-Earth-orbit. Past studies have shown that the quantum character of the cat state can be preserved after CV teleportation, even when taking into account the detector efficiency. However, the channel transmission loss has not been taken into consideration. Traditionally, opti…
Integrated Generation and Purification of Entangled Coherent States for Non-Gaussian Teleportation
本文提出了一种集成光子方案，通过光子子traction和催化生成高保真度的非高斯纠缠相干态，实现了高保真度的量子 teleportation，超越了经典极限。
Camera-enabled scalable homodyne detection of multimode quantum light
利用CCD相机实现60个光学模式的同时散粒噪声极限正交测量，将本振功率需求降低六个数量级，并验证了多模压缩与纠缠。
Quantum Schrodinger cat states are of great interest in quantum communications and quantum optics. These states are used in various scientific fields such as quantum computing, quantum error correction and high-precision measurements. The analysis of the Schrodinger cat states coherence is an important task for their complete practical application. Our developed approach makes it possible to estimate the coherence of the quantum Schrodinger cat state of arbitrary dimension, as well as to find the interference visibility of the state - an important optical characteristic. The obtained simple qu…
Recently Yu and Sun [Int. J. Theor. Phys. DOI 10.1007/s10773-014-2360-x] have presented probabilistic teleportation of 3-qubit cat state via 6-qubit cluster state. The success probability depends on absolute value of only two of the coefficients of cluster state i.e. |c|^2 + |d|^2. We have demonstrated the feasibility to teleport 3-qubit cat state via 2-qubit non maximally entangled Bell state instead of a complex state like 6-qubit non maximally entangled cluster state. In this comment we have prescribed an optimal protocol for teleportation of n-qubit state of the form (α|x> + β|\bar{x}>)_n …
In our work, we compare three teleportation protocols: the original protocol, the photon subtraction protocol, and the protocol with a cubic phase gate. We evaluate the fidelity of each protocol using the example of teleportation of the squeezed state and the Schrodinger's cat state. We show that, under equal conditions, the teleportation scheme with a cubic phase gate achieves significantly higher fidelity than the other protocols considered.
High-Fidelity Quantum State Transfer in Multimode Resonators via Tunable Pulses
本文提出一种双参数控制框架，实现单模到多模交叉区域的高保真量子态传输，通过可调脉冲协议在不需暗态保护或复杂脉冲设计的情况下，达到99.9%以上的传输保真度，并展示了对损耗、杂散、偏移和初始状态不完美的鲁棒性。
Perfect Teleportation and Superdense Coding With W-States
三个量子比特系统状态的真正三方纠缠可以根据随机局域操作和经典通信（SLOCC）进行分类。这种状态可以分为两类：GHZ状态和W状态。众所周知，GHZ态可以用于隐形传态和超密度编码，但原型W态不能。然而，我们发现，有一类W-状态，可以用于完美的隐形传态和超密集编码。
We propose and analyze a setup to tailor the wave functions of the quantum states. Our setup is based on the quantum teleportation circuit, but instead of the usual two-mode squeezed state, two-mode non-Gaussian entangled state is used. Using this setup, we can generate various classes of quantum states such as Schrödinger cat states, four-component cat states, superpositions of Fock states, and cubic phase states. These results demonstrate the versatility of our system as a state generator and suggest that conditioning using homodyne measurements is an important tool in the generations of the…
Entangled coherent states for multiple bosonic modes, also referred to as multimode cat states, not only are of fundamental interest, but also have practical applications. The nonclassical correlation among these modes is well characterized by the violation of the Mermin-Klyshko inequality. We here study Mermin-Klyshko inequality violations for such multi-mode entangled states with rotated quantum-number parity operators. Our results show that the Mermin-Klyshko signal obtained with these operators can approach the maximal value even when the average quantum number in each mode is only 1, and …
Unidirectional Cyclic Quantum Teleportation of Arbitrary Schrodinger Cat Coherent-states via Bell Coherent-States
该研究以三个 Bell 相干态簇为信道，结合线性光学器件与光子数分辨探测，实现三方间任意薛定谔猫相干态的单向循环量子隐形传态，并分析保真及近保真情形的成功概率。
Quantum teleportation is the transfer of quantum information between two locations by the use of shared entanglement. Current teleportation schemes broadly fall under one of two categories, of either qubit or continuous variables teleportation. Spin coherent states on spin ensembles can be teleported under the continuous variables approximation for states with small deviations from a given polarization. However, for spin coherent states with large deviations, no convenient teleportation protocol exists. Recently, we introduced a teleportation scheme where a spin coherent state lying on the equ…
We address fundamental limitations of quantum teleportation -- the process of transferring quantum information using classical communication and preshared entanglement. We develop a new teleportation protocol based upon the idea of using ancillary entanglement catalytically, i.e. without depleting it. This protocol is then used to show that catalytic entanglement allows for a noiseless quantum channel to be simulated with a quality that could never be achieved using only entanglement from the shared state, even for catalysts with a small dimension. On the one hand, this allows for a more faith…
Entangled coherent states: teleportation and decoherence
当两个相位相反的相干态的叠加态$(|α>-|-α>)$落在50-50分束器上时，所得到的态是纠缠的。值得注意的是，纠缠量正好是1 ebit，与$α$无关，正如O. Hirota和M.佐佐木在这里，我们讨论了这种状态的退相干特性，并给出了一个简单的协议，传送一个量子比特编码的薛定谔猫态
We present a linear optical protocol for teleporting and correcting both temporal and frequency errors in two time-frequency qubit states. The first state is the frequency (or time-of-arrival) cat qubit, which is a single photon in a superposition of two frequencies (or time-of-arrival), while the second is the time-frequency Gottesman-Kitaev-Preskill (GKP) state, which is a single photon with a frequency comb structure. The proposed optical scheme could be valuable for reducing error rate in quantum communication protocols involving one of these qubits.
Asymptotic teleportation schemes bridging between standard and port-based teleportation
本文提出一种渐近隐形传态方案，通过联合测量变换连接标准与端口基隐形传态，分类解析量子比特协议并扩展到高维系统，为量子网络发展提供新途径。
Quantum superpositions of coherent states are produced both in microwave and optical domains, and are considered realizations of the famous "Schrödinger cat" state. The recent progress shows an increase in the number of components and the number of modes involved. Our work creates a theoretical framework for treatment of multicomponent two-mode Schrödinger cat states. We consider a class of single-mode states, which are superpositions of $N$ coherent states lying on a circle in the phase space. In this class we consider an orthonormal basis created by rotationally-invariant circular states (RI…
We present a comprehensive investigation of nonideal continuous-variable quantum teleportation implemented with entangled non-Gaussian resources. We discuss in a unified framework the main decoherence mechanisms, including imperfect Bell measurements and propagation of optical fields in lossy fibers, applying the formalism of the characteristic function. By exploiting appropriate displacement strategies, we compute analytically the success probability of teleportation for input coherent states, and two classes of non-Gaussian entangled resources: Two-mode squeezed Bell-like states (that includ…
Growth of Schrödinger cats in particle-number measurement schemes
研究基于多模高斯态的光子数分辨测量生成压缩薛定谔猫态，推导两模和三模方案的状态解析表达式及保真度公式，分析振幅与探测粒子数的标度关系，并给出保真度上限及多模方案提升条件。
The entanglement structure between different frequency components within broadband quantum light pulses, forged at entanglement creation, represents a promising route to the practical delivery of many multipartite quantum information applications. However, the scalability of such applications is largely limited by the entanglement decoherence caused by photon loss. One promising method to combat such losses is noiseless linear amplification. However, while there have been various procedures that implement noiseless linear amplification on single-mode states, no realization has thus far been pr…
Continuous variable quantum teleportation with sculptured and noisy non-Gaussian resources
我们研究了利用辐射场的相关类非高斯态作为纠缠源的连续变量量子隐形传态。首先，我们介绍了双模压缩对称叠加Fock态，包括双光束高斯态的有限截断作为特殊实现。这些状态依赖于一组自由的独立参数，可以调整的隐形传态协议的优化，与增强的成功概率的隐形传态的相干和Fock输入状态。我们发现，优化过程减少了纠缠资源截断双光束状态，从而代表了一类最佳的非高斯资源的量子隐形传态。然后，我们引入了另一类双模非高斯纠缠资源，压缩猫状态的形式。我们分析了优化（CV）隐形传态时的性能和性质，并将它们与以前的工作\cite{CVTelepNoi}中引入的优化压缩Bell态进行比较。我们讨论了如何最佳资源的隐形传态的特点是一个适当的平衡的纠缠内容和压缩真空亲和力。最后研究了热噪声对量子隐形传态效率的影响。为此，一个方便的框架是将噪声纠缠资源描述为非高斯态和热态的线性叠加。虽然热分量的存在大大降低了隐形传态的保真度，但与嘈杂的双光束高斯态相比，嘈杂的非高斯态仍然是首选资源。
We present a detailed analytic framework for studying multimode non-Gaussian states that are conditionally generated when few modes of a multimode Gaussian state are subject to photon-number-resolving detectors. From the output state Wigner function, we deduce that the state factorizes into a Gaussian gate applied to a finite Fock-superposition non-Gaussian state. The framework provides an approach to find the optimal strategy to generate a given target non-Gaussian state. We explore examples, such as the generation of cat states, weak cubic phase states, and bosonic code states, and achieve i…
Accessing continuous-variable entanglement witnesses with multimode spin observables
本研究提出基于多模自旋可观测量的连续变量纠缠检测方案，借助Jordan-Schwinger映射将纠缠判据转化为可通过少量光子数测量实现的形式，无需量子态层析即可高效检测多种态的纠缠，且实验缺陷影响适中。
We propose a deterministic scheme for teleporting an unknown qubit through continuous-variable entangled states in superconducting circuits. The qubit is a superconducting two-level system and the bipartite quantum channel is a photonic entangled coherent state between two cavities. A Bell-type measurement performed on the hybrid state of solid and photonic states brings a discrete-variable unknown electronic state to a continuous-variable photonic cat state in a cavity mode. This scheme further enables applications for quantum information processing in the same architecture of circuit-QED suc…
Time-Frequency Continuous-Variable Quantum Teleportation with Single Photons
本研究提出单光子时频连续变量量子隐形传态协议，明确探测器位置作为时间参考的要求，推导保真度阈值，可用于远程探测器同步，为量子通信远程同步提供方向。
Generation of multicomponent Schrödinger cat states in schemes with measurement of Gaussian states
本研究提出基于多模高斯态光子数分辨测量的方案，产生粒子数差4或8的福克态叠加态，经与多组分薛定谔猫态对比，评估保真度缩放规律并推导最优配置。
The coherent transduction between microwave and optical frequencies is critical to interconnect superconducting quantum processors over long distances. However, it is challenging to establish such a quantum interface with high efficiency and small added noise based on the standard direct conversion scheme. Here, we propose a transduction scheme based on continuous-variable quantum teleportation. Reliable quantum information transmission can be realized with an arbitrarily small cooperativity, in contrast to the direct conversion scheme which requires a large minimum cooperativity. We show that…
Teleporting two-qubit entanglement across 19 qubits on a superconducting quantum computer
本文在127量子比特IBM Quantum设备上实现跨越19个量子比特的两量子比特纠缠隐形传态，比较了后选择测量分类和动态电路修正两种方法，发现基于负性纠缠度量的路径选择在维持纠缠方面优于门错误图。
Near-term quantum computers can hold only a small number of qubits. One way to facilitate large-scale quantum computations is through a distributed network of quantum computers. In this work, we consider the problem of distributing quantum programs represented as quantum circuits across a quantum network of heterogeneous quantum computers, in a way that minimizes the overall communication cost required to execute the distributed circuit. We consider two ways of communicating: cat-entanglement that creates linked copies of qubits across pairs of computers, and teleportation. The heterogeneous c…
Heterogeneous quantum networks consisting of mixed-technologies - Continuous Variable (CV) and Discrete Variable (DV) - will become ubiquitous as global quantum communication matures. Hybrid quantum-entanglement between CV and DV modes will be a critical resource in such networks. A leading candidate for such hybrid quantum entanglement is that between Schrödinger-cat states and photon-number states. In this work, we explore the use of Two-Mode Squeezed Vacuum (TMSV) states, distributed from satellites, as a teleportation resource for the re-distribution of our candidate hybrid entanglement pr…
Gaussian entanglement and quantum communication: geodesic optimization and multimode bounds
该研究针对光量子通信中损耗与噪声问题，开发框架计算高斯受限的相对熵纠缠与Rains纠缠，提出凸主化算法并通过数值方法得到通信界，还给出光子数截断方法计算无限制纠缠量。
Symmetry-resolved parent Hamiltonians for entangled bosonic cat resources
研究多模玻色子猫态资源态的母哈密顿量，通过振荡器算子构建，分离通用分支哈密顿量与状态相关约束哈密顿量，去除低能流形简并，给出多种猫态的显式母哈密顿量，搭建相干态与量子信息处理间桥梁。
We present an algorithm to reliably generate various quantum states critical to quantum error correction and universal continuous-variable (CV) quantum computing, such as Schrödinger cat states and Gottesman-Kitaev-Preskill (GKP) grid states, out of Gaussian CV cluster states. Our algorithm is based on the Photon-counting-Assisted Node-Teleportation Method (PhANTM), which uses standard Gaussian information processing on the cluster state with the only addition of local photon-number-resolving measurements. We show that PhANTM can apply polynomial gates and embed cat states within the cluster. …
Optomagnonic continuous-variable quantum teleportation enhanced by non-Gaussian distillation
针对光磁耦合弱导致的量子隐形传态保真度低问题，提出引入非高斯蒸馏操作增强光磁纠缠的光磁连续变量量子隐形传态协议，可传输多种光态至磁子模式，为磁子量子网络提供指导并开辟磁子量子态制备新途径。
Topological Quantum Teleportation and Superdense Coding -- Without Braiding
针对 Tambara–Yamagami 任意子理论，本文提出无需编织的量子隐形传态与超密编码协议，降低对准粒子的控制需求，并可兼容一维量子线 Majorana 模式。
A categorical semantics of quantum protocols
我们从一个新的角度研究量子信息和计算。我们的方法是基于重铸的标准公理介绍的量子力学，由于冯诺依曼，在一个更抽象的层次上，紧凑的封闭范畴的双产品。我们展示了如何在关键的量子信息协议，如隐形传态，逻辑门隐形传态和纠缠交换中发现的基本结构可以在这个抽象的层次上被捕获。此外，从紧闭包和双积的--显然是纯定性的--结构的组合中，出现了“标量”和“玻恩规则”。这种抽象和结构的观点为描述和推理量子系统开辟了新的可能性。它还显示了公理自由度：我们可以显示对标量C（I，I）的（半）环的要求，其中C是范畴，I是张量单位，以执行各种协议，如隐形传态。我们的形式主义捕捉了协议的信息流方面（见quant-ph/0402014），以及由于量子不确定性而产生的分支。这与标准解释形成对比，在标准解释中，经典信息流“在”通常的量子力学形式主义之外。
Bipartite and Multipartite Entanglement of Gaussian States
在这一章中，我们回顾了连续变量系统高斯态纠缠的表征。对于双模高斯态，我们讨论了它们的二分纠缠如何可以准确地量化的整体和局部的混合量，并有效地估计直接测量相关的纯度。对于多模高斯态，赋予局部对称性相对于一个给定的双分区，我们展示了如何多模块纠缠可以完全和可逆地本地化到一个单一的模式对本地，酉操作。然后我们分析了多模高斯态中多方纠缠的分布。我们引入连续变量纠缠来量化高斯态中的纠缠共享，并证明了它满足Coffman-Kundu-Wootters一夫一妻不等式。然而，我们发现，纯的，对称的三模高斯态，在与离散变量对应的差异，允许混杂的共享量子相关性，表现出最大的三方剩余纠缠和最大耦合纠缠之间的任何一对模式。最后，我们研究了连续变量量子隐形传态网络中多体纠缠与最佳保真度之间的关系。我们展示了如何保真度可以最大化的共享纠缠资源的最佳准备方面，反之亦然，这种最佳保真度提供了一个明确的操作解释的几个措施的二分和多分纠缠，包括纠缠的形成，本地化纠缠，和连续变量纠缠。
Entanglement catalysis for quantum states and noisy channels
本工作研究了纠缠催化在量子通信中的作用，证明了双方纯态变换中通用催化剂的存在，并开发了有噪量子信道辅助下估计单重态数量的方法，导出了单次使用信道建立最大单重态的最优协议。
Approximate transformations and robust manipulation of bipartite pure state entanglement
我们分析了纯纠缠量子态通过局域操作和经典通信的近似变换，找到了优化变换保真度的显式变换策略。这些结果使我们能够通过初始共享的部分纠缠纯态来确定最忠实的隐形传态策略。他们还表明，纠缠操纵的程序，如纠缠催化[乔纳森和Plenio，物理Rev.Lett。83，3566（1999）]对所涉及的状态的扰动是鲁棒的，并且激发了非局域保真度的概念，其量化了两个量子态的纠缠特性的差异。
The cat code is a promising encoding scheme for bosonic quantum error correction as it allows for correction against losses--the dominant error mechanism in most bosonic systems. However, for losses to be detected efficiently without disturbing the encoded logical information, one needs to implement a parity measurement of the excitation number. While such a measurement has been demonstrated in the microwave regime using a superconducting transmon ancilla, it has remained unclear how it can be implemented in the optical regime. Here, we introduce a teleportation-based error-correction scheme f…
Schrödinger's thought experiment to prepare a cat in a superposition of both alive and dead states reveals profound consequences of quantum mechanics and has attracted enormous interests. Here we propose a straightforward method to create quantum superposition states of a living microorganism by putting a small cryopreserved bacterium on top of an electromechanical oscillator. Our proposal is based on recent developments that the center-of-mass oscillation of a 15-$μ$m-diameter aluminium membrane has been cooled to its quantum ground state [Nature 475: 359 (2011)], and entangled with a microwa…
Catalytic and asymptotic equivalence for quantum entanglement
本文研究量子纠缠的催化与渐近操作，证明两者对所有可蒸馏态完全等价，并发现使用纠缠催化剂无法提升渐近单态蒸馏率，突出了多拷贝相关性的关键作用。
We propose a deterministic remote state preparation (RSP) scheme for preparing an arbitrary (including pure and mixed) qubit, where a partially entangled state and finite classical communication are used. To our knowledge, our scheme is the first RSP scheme that fits into this category. One other RSP scheme proposed by Berry shares close features, but can only be used to prepare an arbitrary pure qubit. Even so, our scheme saves classical communication by approximate 1 bit per prepared qubit under equal conditions. When using a maximally entangled state, the classical communication for our sch…
Barut-Girardello coherent states for u(p,q) and sp(N,R) and their macroscopic superpositions
将Barut-Girardello相干态（BG CS）表示推广到非紧代数u（p，q）和sp（N，R）的（可约）二次玻色子实现. sp（N，R）BG CS采取多模普通薛定谔猫态的形式。2^{n-1} sp（N，R）CS（2 ^n正则CS，n= 1，2，.）指出了N-模Hilbert空间中的超完备性，并建立了正则CS与u（p，q）BG型CS表示之间的关系. u（p，q）和sp（N，R）BG CS的集合及其离散叠加包含了量子光学中研究的许多态（偶和奇N模CS，对CS），并提供了一种替代智能态的正交压缩方法。指出了新的弱非经典态和强非经典态的子集，并讨论了它们的统计性质（一阶和二阶压缩，光子数分布）。对于特定值的角度参数和小振幅的正则CS分量，这些状态接近多模Fock状态与一个，两个或三个玻色子/光子。结果表明，平方非厄米算符A^2的本征态（广义猫态）可以表现出A的平方的压缩。
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