Schrodinger Cat States for Quantum Information Processing
H. Jeong, T. C. Ralph
我们广泛地讨论了光学系统中薛定谔猫态（分离相干态的叠加）如何用于量子信息处理。
We extensively discuss how Schrodinger cat states (superpositions of well-separated coherent states) in optical systems can be used for quantum information processing.
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We present novel theory of effective realization of large-scale optical Schrodinger cat states.
We analyze condition of orthogonality between optical Schrodinger cat-like-states constructed as superposition of two coherent states. We show that the orthogonality condition leads to quantization of values of a naturally emerging symplectic form, while values of the corresponding metric form are continuous. A complete analytical solution of the problem is presented.
Photon Statistics for MUltimode Squeezed Schrödinger Cat States
用多变量厄米多项式给出了压缩态、偶相干态和奇相干态中的粒子分布。讨论了非经典场态的Q函数和Wigner函数。
Does Schrodinger's Cat Know Something That Schrodinger Does Not Know?
宏观物体似乎有确定的位置。在量子理论的多世界解释中，这种现象是一种幻觉;正确的观点是“从外部看”，在这种观点中，甚至宏观物体一般也处于不同位置的叠加。在玻姆模型中，物体确实处于确定的位置。现实的这个附加方面只能从“内部”进入;因此在玻姆模型中，从内部的观点可能比从外部的观点更正确。
EPR, Bell, Schrodinger's cat, and the Monty Hall Paradox
这份手稿的目的是提供一个简短的教学解释，为什么“量子崩溃”不是一个形而上学事件，通过指出与蒙蒂霍尔帕萨特相关的“经典崩溃”的类比。
Engineering Schrödinger cat states through cavity-assisted interaction of coherent optical pulses
我们提出了一个方案，工程薛定谔猫传播光脉冲的状态。通过连续反射相干光脉冲，可以在单原子腔中产生多维多粒子猫态。通过详细的数值模拟，分析了原子自发发射和脉冲波形畸变等噪声源对激光器输出的影响，验证了该方案在现有实验技术条件下的实用性。
Twelve-spin "Schrodinger cat"
实验证明了13 C标记苯分子在液晶基质中的12个偶极耦合核自旋系统的赝纯“猫”态，即所有自旋向上和所有自旋向下的量子态的叠加态.
The manuscript investigates the entropy squeezing of a qubit (two-level atom) interacting with the cavity field in the Schrödinger cat states. The effects of the Schrödinger cat states of the field on the squeezing are examined. Our results suggest that entropy squeezing is not sensitive to the superposition features of two coherent states of the Schrödinger cat states. Furthermore, it is found that entropy squeezing occurs as the qubit initially close to its maximally coherent state, and the qubit initially in the maximally coherent state can generate optimal squeezing. This also demonstrates…
From the following thought experiments, it is demonstrated that the collapse of wave function of an isolated system is possible without external observer. It will be shown that the analysis by Feynman path integral method supports this conclusion. The argument is based on two assumptions: 1. The condition of Schrodinger's cat experiment 2. Feynman path integral; This could explain Schrodinger's cat paradox and its implication on the black hole information paradox will be discussed.
Barut-Girardello coherent states for sp(N,C) and multimode Schrödinger cat states
对二次玻色子表示下的非紧代数$u(p,q)$和$sp(N,C)$构造了Barut-Girardello相干态（BG CS）型的过完备态族. $sp(N,C)$ BG CS是以多模普通薛定谔猫态的形式得到的。一组这样的宏观叠加指出，这是在整个$N$模式希尔伯特空间过完备（而相关的$sp(N,C)$表示是可约的）。多模平方振幅薛定谔猫态被引入作为所获得的$sp(N,C)$ BG CS的宏观叠加。
In addition to being a very interesting quantum phenomenon, Schrödinger cat swapping has the potential for application in the preparation of quantum states that could be used in metrology and other quantum processing. We study in detail the effects of field decoherence on a cat-swapping system comprising a set of identical qubits, or spins, all coupled to a field mode. We demonstrate that increasing the number of spins actually mitigates the effects of field decoherence on the collapse and revival of a spin Schrödinger cat, which could be of significant utility in quantum metrology and other q…
Schrödinger cat states, consisting of superpositions of macroscopically distinct states, provide key resources for a large number of emerging quantum technologies in quantum information processing. Here we propose how to generate and manipulate mechanical and optical Schrödinger cat states with distinguishable superposition components by exploiting the unique properties of cavity optomechanical systems based on Bose-Einstein condensate. Specifically, we show that in comparison with its solid-state counterparts, almost a $3$ order of magnitude enhancement in the size of the mechanical Schröding…
Wehrl information entropy and phase distributions of Schrodinger cat and cat-like states
Wehrl信息熵及其相位密度，即所谓的Wehrl相位分布，被用来描述薛定谔猫态和类猫态。在描述叠加原理时，给出了Wehrl相位分布相对于Wehrl熵的优点。熵的措施进行了比较与传统的相位分布从胡西米Q函数。对于分离好的态的叠加，得到了熵测度的紧致形式公式。详细分析了薛定谔猫态（包括偶、奇和Yurke-Sternberg相干态）以及克尔介质中产生的类猫态的例子。结果表明，在对比的Wehrl熵，Wehrl相位分布正确区分不同的叠加不等权的状态，就其数量和相空间配置。
Schrodinger cats and their power for quantum information processing
我们概述了一个工具箱，包括被动光学元件，单光子探测和叠加的相干态（薛定谔猫态）。这样的工具箱是用于量子信息处理任务的强大基元集合。我们通过概述一个通用量子计算的建议来说明它的用途。我们利用这个工具箱的量子精密测量的应用，例如弱力测量和精确的相位估计。我们表明，在这两种情况下，在海森堡极限的灵敏度是可以实现的。
Preparation of Schrödinger cat quantum state using parametric down-conversion interaction
本研究针对量子光学中薛定谔猫态的制备需求，提出一种基于简并参量下转换与泵浦模式光子数预示测量的亮多光子薛定谔猫态条件生成新方法，且该方法原则上可通过现有高Q光学微谐振器实现。
Schrodinger's famous cat has long been misunderstood. According to quantum theory and experiments with entangled systems, an entangled state such as the Schrodinger's cat state is neither a superposition of states of either subsystem nor a superposition of compound states of the composite system, but rather a nonlocal superposition of correlations between pairs of states of the two subsystems. The entangled post-measurement state that results from an ideal measurement is not paradoxical, but is merely a coherent superposition of two statistical correlations at "zero phase angle," i.e. at 100% …
The marginal distribution of squeezed, rotated and shifted quadrature for two types of nonclassical states of a trapped ion - squeezed correlated states and squeezed even and odd coherent states (squeezed Schrodinger cat states) - is studied.
We carry out probabilistic phase-space sampling of mesoscopic Schrödinger cat quantum states, demonstrating multipartite Bell violations for up to 60 qubits. We use states similar to those generated in photonic and ion-trap experiments. These results show that mesoscopic quantum superpositions are directly accessible to probabilistic sampling, and we analyze the properties of sampling errors. We also demonstrate dynamical simulation of super-decoherence in ion traps. Our computer simulations can be either exponentially faster or slower than experiment, depending on the correlations measured.
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。
What Schrödinger's Cat is Telling
最近的超导量子干涉实验为阐明量子力学的基本解释提供了新的契机。通过对这一点和相关实验的分析，我们提出了这样的观点：抽象意义上的量子态不含信息，波函数是观测者准备进行的与真实测量相对应的虚拟测量的概率幅。用普通的语言谈论量子态或波函数过于具体化，往往会引起误解。所以基本上，薛定谔的猫悖论结束了。
In recent years, there has been an increased interest in the generation of superposition of coherent states with opposite phases, the so-called photonic Schrodinger-cat states. These experiments are very challenging and so far, cats involving small photon numbers only have been implemented. Here, we propose to consider two-mode squeezed states as examples of a Schrodinger-cat-like state. In particular, we are interested in several criteria aiming to identify quantum states that are macroscopic superpositions in a more general sense. We show how these criteria can be extended to continuous vari…
Investigated idea was actuated by the old opinion that a measurement of a quantum observable should be regarded a as a single deterministic sampling. But, according to the last decades studies, such observables are veritable random variables and their measurements must imply significant sets of statistical samplings. So one finds the indubitable caducity of the approached idea. Contiguously the respective finding allows to put into a new light the controversial questions like the Schrodinger's cat thought experiment or description of quantum measurements.
Quantum effects and, in particular, entanglement are by now widely recognized in all areas of physics and related fields. However, we feel that the precise notion of entanglement---though mathematically well-defined---still generates confusion even in the academic environment. Our aim in this article is to point out and clarify some aspects of the notion of entanglement, in particular with respect to observable quantities. We do this by illustrating common misconceptions with Schrödinger's cat paradox, explain them in mathematical terms and provide examples where misunderstandings arise and ho…
We discuss general properties of the equilibrium state of parametric down-conversion in superconducting quantum circuits with detunings and Kerr anharmonicities, in the strongly nonlinear regime. By comparing moments of the steady state and those of a Schrödinger cat, we show that true Schrödinger cats cannot survive in the steady state if there is any single-photon loss. A delta-function 'cat-like' steady-state distribution can be formed, but this only exists in the limit of an extremely large nonlinearity. The steady state is a mixed state, which is more complex than a mixture or linear comb…
Homodyne measurements are a widely used quantum measurement. Using a coherent state of large amplitude as the local oscillator, it can be shown that the quantum homodyne measurement limits to a field quadrature measurement. In this work, we give an example of a general idea: injecting non-classical states as a local oscillator can led to non-classical measurements. Specifically we consider injecting a superposition of coherent states, a Schrödinger cat state, as a local oscillator. We derive the Kraus operators and the positive operator-valued measure (POVM) in this situation.
Wigner Distribution Analysis of a Schrodinger Cat Superposition of Displaced Equilibrium Coherent States
受最近实验的启发，我们考虑了两个相距很远的相干态在热平衡下的薛定谔猫叠加。我们的系统的时间发展得到使用维格纳分布函数。与我们对双高斯波包的讨论相反[Phys. Lett. A286（2001）87]，我们发现，在没有耗散的情况下，干扰项并不随时间迅速衰减，但与其他两项一样，它随时间振荡并持续所有时间
Schrödinger's cat originates from the famous thought experiment querying the counterintuitive quantum superposition of macroscopic objects. As a natural extension, several "cats" (quasi-classical objects) can be prepared into coherent quantum superposition states, which is known as multipartite cat states demonstrating quantum entanglement among macroscopically distinct objects. Here we present a highly scalable approach to deterministically create flying multipartite Schrödinger cat states, by reflecting coherent state photons from a microwave cavity containing a superconducting qubit. We per…
Probing gravity-related decoherence with a 16 $μ$g Schrödinger cat state
本研究通过16微克机械谐振子的薛定谔猫态退相干实验，检验了与引力相关的Diósi-Penrose波函数坍缩模型，探讨宏观叠加态破坏的机制。
Quantum superpositions of distinct coherent states in a single-mode harmonic oscillator, known as "cat states", have been an elegant demonstration of Schrodinger's famous cat paradox. Here, we realize a two-mode cat state of electromagnetic fields in two microwave cavities bridged by a superconducting artificial atom, which can also be viewed as an entangled pair of single-cavity cat states. We present full quantum state tomography of this complex cat state over a Hilbert space exceeding 100 dimensions via quantum non-demolition measurements of the joint photon number parity. The ability to ma…
Schrodinger's cat: The rules of engagement
在以前的论文中，我们研究了一个有意识的观察者在一个典型的量子力学测量中的作用。给出了四条规则，发现在连续和间歇观测的几种情况下，这些规则支配随机选择和状态归约。它表明，意识总是伴随着导致观察的状态还原，但它的存在不足以“导致”还原。下文重复的规则澄清和编纂了这一区别。在本文中，这些规则被成功地应用到两个不同版本的薛定谔猫实验。关键词：大脑状态，边界条件，猫悖论，意识，有意识的观察者，环境，退相干，宏观叠加，测量，状态归约，状态崩溃，冯·诺依曼。
The Schrödinger cat state plays a crucial role in quantum theory, and has important fundamental as well as technological implications, ranging from quantum measurement theory to quantum computers. The power of the potential implications of the cat state lies in the quantum coherence, as measured by the degree of entanglement, between its microscopic and macroscopic sectors. We show that in contrast to other cat states, it is possible to choose the states of the macroscopic sector in a way that the resulting cat state, which we term as the W-cat state, has quantum coherence that is resistant to…
In this paper, we are interested in detecting the presence of a nearby phase-sensitive object, where traveling light works out under a low-photon loss rate. Here we investigate the optimal quantum phase estimation with generalized multi-component Schrodinger cat states. In addition, we show the optimal conditions of the generalized multi-component cat states for the phase estimation in a lossless scenario. We then demonstrate that the generalized multi-component cat states can beat the performances of the NOON and two-mode squeezed vacuum states in the presence of small loss, while maintaining…
Spin-dependent forces on trapped ions for phase-stable quantum gates and motional Schrodinger-cat states
用于捕获离子量子逻辑门的FIGH方案使用双色激光场通过“自旋相关力”将内部量子比特态与外部运动耦合。“我们在这种耦合中引入了一个新的自由度，降低了它对相位退相干的敏感性。我们证明了一个单一的捕获$^{111}$镉$^+$离子的双色自旋相关的力量，并显示所产生的“薛定谔猫”运动状态的相位相干性取决于光谱的光场的安排。这直接适用于多个离子上的纠缠门的操作。
Given a source of two coherent state superpositions with small separation in a traveling wave optical setting, we show that by interference and balanced homodyne measurement it is possible to conditionally prepare a symmetrically placed superposition of coherent states around the origo of the phase space. The separation of the coherent states in the superposition will be amplified during the process.
A measurement-induced continuous-variable logical gate is able to prepare Schrödinger cat states if the gate uses a non-Gaussian resource state, such as cubic phase state [I. V. Sokolov, Phys. Lett. A 384, 126762 (2020)]. Our scheme provides an alternative to hybrid circuits which use photon subtraction and (or) Fock resource states and photon number detectors. We reveal the conditions under which the gate conditionally prepares quantum superposition of two undistorted "copies" of an arbitrary input state that occupies a finite area in phase space. A detailed analysis of the fidelity between t…
In order to know if the Schrodinger's cat is alive or dead without opening the box, observers have to play a game with nature. The observers have to "guess" (with degrees of belief) the state of the cat due to incomplete information; in other words, the observers' decision has to be made under uncertainty. We propose a quantum expected value theory for decision-making under uncertainty. Value operator is proposed to guide observers to choose corresponding actions based on their subjective beliefs through objective quantum world by maximizing the value from the measured historical results. The …
Optimizing for an arbitrary Schrödinger cat state. II. Application in the presence of dissipation
本文将针对任意猫态的优化泛函扩展至开放量子系统，应用于存在衰减的 Jaynes-Cummings 模型，发现在强耗散和大猫半径下制备纠缠猫态的控制策略发生改变，展示了量子最优控制工具箱在量子技术中的实用性。
The basic idea here is that observation (or one's experience) is fundamental and the `atomic world' is postulated as the source of such observation. Once this source has been inferred to exist one may attempt to explicitly derive its structure in such a way that the observation itself can be reproduced. And so here is a purely quantum mechanical model of observation coupled to its supposed source, and the observation itself is realised as a projection of this quantum system.
Measurement-induced generation of Schrödinger cat states in cavity QED
该研究在腔-QED系统中提出结合相干驱动、色散原子-腔相互作用和原子后选择的测量方案，可实验可行地产生抗中等腔耗散的薛定谔猫态，无需强光学非线性或工程化耗散。
We propose a non-Gaussian continuous variable (CV) gate which is able to conditionally produce superposition of two "copies" of an arbitrary input state well separated in the coordinate and momentum plane - a Schrödinger cate state. The gate uses cubic phase state of an ancillary oscillator as a non-Gaussian resource, an entangling Gaussian gate, and homodyne measurement which provides nonunique information about the target system canonical variables, which is a key feature of the scheme. We show that this nonuniqueness manifests problems which may arise by extension of the Heisenberg picture …
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…
Collapse and Revival of `Schrödinger Cat' States
研究了$N_q$二能级系统（或量子比特）与量子化单模电磁腔（或量子总线）相互作用的Jaynes-Cummings模型的动力学行为。对于初始腔相干态$| α>$和量子比特系统在其Hilbert空间中的特定“吸引盆”中，我们证明了量子比特系统和场模之间的两个宏观量子态叠加态的振荡.从量子比特或场系统的角度来看，存在“薛定谔猫”状态的崩溃和复兴。
Appearance of Schrodinger Cat States in the Measurement Process
虽然量子力学是一个成熟的理论，但在它创立时所讨论的基本问题至今仍伴随着我们。这些问题集中在量子世界和经典世界之间的问题关系上。最著名的元素是测量问题，即，用经典仪器测量量子系统，以及伴随的波包减少现象，概率的出现，以及与薛定谔猫态有关的问题。在这种背景下，一个基本的问题是量子力学是否可以自举到经典世界：量子力学是自洽的，使得测量过程可以在量子力学本身中理解，还是这个过程需要来自传统量子力学之外的领域的额外元素？在这里，我们指出了传统薛定谔猫论证中的一个有问题的方面，可以通过适当的宏观准备装置来克服它的扩展;猫态的故意创造和识别然后变成了一个非平凡的问题，需要确定与宏观水库纠缠的量子系统的演化。我们描述了一种新型的波函数相关器测试薛定谔猫态的出现，并讨论了它的理论推导的波函数崩溃从一个单一的演变的影响。
Iterative $C_Z$-gate-based protocol for squeezed Schrödinger cat state engineering
提出一种测量辅助门，通过非高斯小振幅压缩猫态辅助和量子非破坏纠缠操作及外差测量，生成高保真度、尺寸可控的压缩薛定谔猫态，并引入迭代外差条件 $C_Z$ 协议实现猫态放大。
We give a mathematical procedure to obtain the adiabatic approximation for the generalized quantum Rabi Hamiltonian both without and with a quadratic interaction. We consider the Hamiltonian as the energy of a model describing the interaction system of a two-level artificial atom and a one-mode microwave photon in circuit QED. In the case without the quadratic interaction, we show in the adiabatic approximation that whether each bare eigenstate forms a Schrodinger-cat-like entangled state or not depends on whether the energy bias of the atom is zero or non-zero, and then, the effect of the tun…
Photon number projective measurement in Schrödinger cat quantum state preparation procedure after parametric down-conversion interaction
本文提出一种基于参数下转换的薛定谔猫态制备方法，通过泵浦耗尽和投影测量提高生成概率，改进了之前的工作。
The interference pattern in electron double-slit diffraction is a hallmark of quantum mechanics. A long standing question for stochastic electrodynamics (SED) is whether or not it is capable of reproducing such effects, as interference is a manifestation of quantum coherence. In this study, we use excited harmonic oscillators to directly test this quantum feature in SED. We use two counter-propagating dichromatic laser pulses to promote a ground-state harmonic oscillator to a squeezed Schrödinger cat state. Upon recombination of the two well-separated wavepackets, an interference pattern emerg…
Effects of a classical homogeneous gravitational field on the cavity-field entropy and generation of the Schrodinger-cat states in the Jaynes-Cummings model
本文研究了引力场对Jaynes-Cummings模型中腔场熵的动力学演化和薛定谔猫态的产生的影响。研究了在经典均匀引力场作用下运动二能级原子与单模量子化腔场的相互作用。以SU（2）代数为动力学对称群，导出了考虑原子运动和引力场影响的腔场约化密度算符.此外，我们还得到了系统状态矢量的精确解和近似解，并研究了原子动力学。在考虑腔场熵随时间的演化以及腔场Q函数动力学的基础上，利用Q函数、场熵和系统态矢量的近似解，研究了引力场对腔场薛定谔猫态产生的影响.结果表明，引力场破坏了腔场薛定谔猫态的产生。
Resonant Schrödinger Cat States in Circuit Quantum Electrodynamics
我们提出一种利用连续驱动量子比特在超导谐振器中快速生成薛定谔猫态的方案，无需色散区域或双光子驱动，并通过解析分析与数值模拟验证了其可行性。
Generation of Four-Component Schrödinger Cat States via Floquet Engineering in a Hybrid Ferromagnet-Superconductor System
针对固态平台难以制备四分量薛定谔猫态的问题，提出混合铁磁体-超导体系统中的 Floquet 工程方案，并证明在退相干下仍可高保真生成该态。
Bosonic quantum codes redundantly encode quantum information in the states of a quantum harmonic oscillator, making it possible to detect and correct errors. Schrödinger cat codes -- based on the superposition of two coherent states with opposite displacements -- can correct phase-flip errors induced by dephasing, but they are vulnerable to bit-flip errors induced by particle loss. Here, we develop a bosonic quantum code relying on squeezed cat states, i.e. cat states made of a linear superposition of displaced-squeezed states. Squeezed cat states allow to partially correct errors caused by pa…
Nonreciprocal Generation of Schrödinger Cat State Induced by Topology
本文提出在一维微腔阵列中利用拓扑保护手性模式激发，实现边缘腔薛定谔猫态的方向选择性非互易产生，并可通过拓扑相变开关控制。
Fast generation of Schrödinger cat states in a Kerr-tunable superconducting resonator
针对三维腔中薛定谔猫态的可扩展性与可控性难题，提出通过快速调制克尔非线性在共面超导电路中生成存储猫态的新方法，96ns内实现89.1%保真度的双组分猫态，为芯片级玻色量子处理器构建提供新路径。
Highly quantum non-linear interactions between different bosonic modes lead to the generation of quantum non-Gaussian states, i.e. states that cannot be written as mixtures of Gaussian states. A paradigmatic example is given by Schroedinger's cat states, that is coherent superpositions of coherent states with opposite amplitude. We here consider a novel quantum non-Gaussianity criterion recently proposed in the literature and prove its effectiveness on Schroedinger cat states evolving in a lossy bosonic channel. We prove that quantum non-Gaussianity can be effectively detected for high values …
Experimental progress with meso- and macroscopic quantum states (i.e., general Schrodinger-cat states) was recently accompanied by theoretical proposals on how to measure the merit of these efforts. So far, experiment and theory were disconnected as theoretical analysis of actual experimental data was missing. Here, we consider a proposal for macroscopic quantum states that measures the extend of quantum coherence present in the system. For this, the quantum Fisher information is used. We calculate lower bounds from real experimental data. The results are expressed as an "effective size", that…
Universal Quantum Gate Set for Multi-Mode Schrödinger Cat States Stabilized by Non-Local Dissipation Engineering
研究利用非局域耗散工程稳定多模薛定谔猫态实现通用量子计算，通过克尔非线性振荡器链及低维描述实现单比特控制，耦合稳定阵列实现纠缠操作，经数值模拟验证，确立其为通用玻色子量子计算潜在架构。
Quantum Metrology: Detection of weak forces using Schrodinger Cat resources
我们研究了简谐振子的非经典态（相干态的叠加）在灵敏力检测中的应用。我们发现，像压缩态的相干态的叠加允许在海森堡极限位移测量的检测。与具有相同平均光子数的单模叠加态相比，纠缠多个相干态的叠加提供了显著的优势。
Optical Schrödinger cat states generation using cubic phase resource state and beamsplitter
本文提出一种基于非对称分束器和三次相位资源态的光学方案，通过零差测量产生具有可控压缩度的薛定谔猫态，并进行了半经典分析与效率比较。
Programmable optical parametric amplifier synthesizer for cubic phase states and amplified Schrodinger cat states
提出一种可编程光学参量放大器合成器，通过催化与非催化配置，实现高保真度三次相位态生成和薛定谔猫态放大，保真度超过0.99。
Circuit quantum electrodynamics ('circuit QED') describes the quantum mechanics and quantum field theory of superconducting electrical circuits operating in the microwave regime near absolute zero temperature. It is the analog of cavity QED in quantum optics with the role of the atoms being played by superconducting qubits. The present lecture notes focus primarily on novel quantum states that can be produced and measured using the strong coupling between an artificial atom and one or more cavities. Of particular importance are Schrodinger cat states of photons. Despite long being considered e…
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