Jae-Seung Lee, A. K. Khitrin
Pseudopure "cat" state, a superposition of quantum states with all spins up and all spins down, is experimentally demonstrated for a system of twelve dipolar-coupled nuclear spins of fully 13C-labeled benzene molecule oriented in a liquid-crystalline matrix.
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We present novel theory of effective realization of large-scale optical Schrodinger cat states.
We extensively discuss how Schrodinger cat states (superpositions of well-separated coherent states) in optical systems can be used for quantum information processing.
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.
Macroscopic objects appear to have definite positions. In a many-worlds interpretation of quantum theory, this appearance is an illusion; the correct view is the "view from outside" in which even macroscopic objects are in general in a superposition of different positions. In the Bohm model, objects really are in definite positions. This additional aspect of reality is accessible only from the "inside"; thus in the Bohm model the view from inside can be more correct than is the view from outside.
The purpose of this manuscript is to provide a short pedagogical explanation why "quantum collapse" is not a metaphysical event, by pointing out the analogy with a "classical collapse" which is associated with the Monty Hall Paradox.
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.
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…
The Wehrl information entropy and its phase density, the so-called Wehrl phase distribution, are applied to describe Schrödinger cat and cat-like (kitten) states. The advantages of the Wehrl phase distribution over the Wehrl entropy in a description of the superposition principle are presented. The entropic measures are compared with a conventional phase distribution from the Husimi Q-function. Compact-form formulae for the entropic measures are found for superpositions of well-separated states. Examples of Schrödinger cats (including even, odd and Yurke-Stoler coherent states), as well as the…
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。
The recent experiment on superconducting quantum interference device provides new opportunity to clarify the fundamental interpretation of quantum mechanics. After analyzing this and relevant experiments, we claim the point of view that the quantum state in abstract sense contains no information and the wave function is the probability amplitude of fictitious measurement corresponding to the real one which is prepared to be done by the observer. Talking about the quantum state or wave function too materialized in ordinary language would often cause misunderstanding. So basically, the Schröding…
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.
Motivated by recent experiments, we consider a Schrödinger cat superposition of two widely separated coherent states in thermal equilibrium. The time development of our system is obtained using Wigner distribution functions. In contrast to our discussion for a two-Gaussian wave packet [Phys. Lett. A 286 (2001) 87], we find that, in the absence of dissipation, the interference term does not decay rapidly in time, but in common with the other two terms, it oscillates in time and persists for all times
This report experimentally demonstrates that the theoretical background of the atom-field scenario points out that the NMR quadrupolar Hamiltonian works as an effective Hamiltonian to generate Schrödinger's cat states in a $2I+1$ low dimensional Hilbert space. The versatility of this nuclear spin setup is verified by monitoring the $^{23}$Na nucleus of a lyotropic liquid crystal sample at the nematic phase. The quantum state tomography and the Wigner quasiprobability distribution function are performed to characterize the accuracy of the experimental implementation.
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。
We study the effects of continuous measurement of the field mode during the collapse and revival of spin Schrödinger cat states in the Tavis-Cummings model of N qubits (two-level quantum systems) coupled to a field mode. We show that a compromise between relatively weak and relatively strong continuous measurement will not completely destroy the collapse and revival dynamics while still providing enough signal-to-noise resolution to identify the signatures of the process in the measurement record. This type of measurement would in principle allow the verification of the occurrence of the colla…
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…
In a previous paper we examined the role of a conscious observer in a typical quantum mechanical measurement. Four rules were given that were found to govern the stochastic choice and state reduction in several cases of continuous and intermittent observation. It was shown that consciousness always accompanies a state reduction leading to observation, but its presence is not sufficient to 'cause' a reduction. The distinction is clarified and codified by the rules that are repeated below. In this paper, these rules are successfully applied to two different versions of the Schrodinger cat experi…
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…
Favored schemes for trapped-ion quantum logic gates use bichromatic laser fields to couple internal qubit states with external motion through a "spin-dependent force." We introduce a new degree of freedom in this coupling that reduces its sensitivity to phase decoherence. We demonstrate bichromatic spin-dependent forces on a single trapped $^{111}$Cd$^+$ ion, and show that phase coherence of the resulting "Schrödinger-cat" states of motion depends critically upon the spectral arrangement of the optical fields. This applies directly to the operation of entangling gates on multiple ions.
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 the late 80's, Ou and Mandel experimentally observed signal beatings by performing a non-time resolved coincidence detection of two photons having interfered in a balanced beam splitter [Phys. Rev. Lett 61, 54 (1988)]. In this work, we provide a new interpretation of the fringe pattern observed in this experiment as the direct measurement of the chronocyclic Wigner distribution of a frequency Schrödinger cat-like state produced by local spectral filtering. Based on this analysis, we also study time-resolved HOM experiment to measure such frequency state.
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.
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…
We study the dynamics of the Jaynes-Cummings Model for an array of $N_q$ two level systems (or qubits) interacting with a quantized single mode electromagnetic cavity (or quantum bus). For an initial cavity coherent state $| α>$ and the qubit system in a specified `basin of attraction' in its Hilbert space, we demonstrate the oscillation of a superposition of two macroscopic quantum states between the qubit system and the field mode. From the perspective of either the qubit or the field system, there is collapse and revival of a `Schrödinger Cat' state.
Although quantum mechanics is a mature theory, fundamental problems discussed during its time of foundation have remained with us to this day. These problems are centered on the problematic relation between the quantum and classical worlds. The most famous element is the measurement problem, i.e., the measurement of a quantum system by a classical apparatus, and the concomitant phenomena of wave packet reduction, the appearance of probability, and the problems related to Schrödinger cat states. A fundamental question in this context is whether quantum mechanics can bootstrap itself to the clas…
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…
We outline a toolbox comprised of passive optical elements, single photon detection and superpositions of coherent states (Schrodinger cat states). Such a toolbox is a powerful collection of primitives for quantum information processing tasks. We illustrate its use by outlining a proposal for universal quantum computation. We utilize this toolbox for quantum metrology applications, for instance weak force measurements and precise phase estimation. We show in both these cases that a sensitivity at the Heisenberg limit is achievable.
In this paper, we examine the effects of the gravitational field on the dynamical evolution of the cavity-field entropy and the creation of the Schrodinger-cat state in the Jaynes-Cummings model. We consider a moving two-level atom interacting with a single mode quantized cavity-field in the presence of a classical homogeneous gravitational field. Based on an su(2) algebra, as the dynamical symmetry group of the model, we derive the reduced density operator of the cavity-field which includes the effects of the atomic motion and the gravitational field. Also, we obtain the exact solution and th…
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。
A scheme is proposed to prepare squeezed states and Schrödinger cat-like states of the collective spin degrees of freedom associated with a pair of ground states in an atomic ensemble. The scheme uses an effective Jaynes-Cummings interaction which can be provided by excitation of the atoms to Rydberg states and an effective J_x interaction implemented by a resonant Raman coupling between the atomic ground states. Both dynamical evolution with a constant Hamiltonian and with adiabatic variation of the two interaction terms are studied. We show that by the application of further resonant laser f…
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。
We investigate the utility of non classical states of simple harmonic oscillators (a superposition of coherent states) for sensitive force detection. We find that like squeezed states a superposition of coherent states allows the detection of displacement measurements at the Heisenberg limit. Entangling many superpositions of coherent states offers a significant advantage over a single mode superposition states with the same mean photon number.
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…
This communication is an enquiry into the circumstances under which entropy and subentropy methods can give an answer to the question of quantum entanglement in the composite state. Using a general quantum dynamical system we obtain the analytical solution when the atom initially starts from its excited state and the field in different initial states. Different features of the entanglement are investigated when the field is initially assumed to be in a coherent state, an even coherent state (Schrodinger cate state) and a statistical mixture of coherent states. Our results show that the setting…
We summarize efforts at NIST to implement quantum computation using trapped ions, based on a scheme proposed by J.I. Cirac and P. Zoller (Innsbruck University). The use of quantum logic to create entangled states, which can maximize the quantum-limited signal-to-noise ratio in spectroscopy, is discussed.
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