Non-Gaussianity dynamics of two-mode squeezed number states subject to different types of noise based on cumulant theory

We provide a measure to characterize the non-Gaussianity of phase-space function of bosonic quantum states based on the cumulant theory. We study the non-Gaussianity dynamics of two-mode squeezed number states by analyzing the phase-averaged kurtosis for two different models of decoherence: amplitude damping model and phase damping model.For the amplitude damping model, the non-Gaussianity is very fragile and completely vanishes at a finite time. For the phase damping model, such states exhibit rich non-Gaussian characters. In particular, we obtain a transition time that such states can transform from sub-Gaussianity into super-Gaussianity during the evolution. Finally, we compare our measure with the existing measures of non-Gaussianity under the independent dephasing environment.     

利用累积量理论量化双模压缩贝尔态的非高斯特性

根据相空间函数的累积量理论,提出了玻色量子态非高斯性的量化工具.利用该量具研究了四个压缩贝尔纠缠态的非高斯特性.结果表明:高斯操作能显著的改变这些态的非高斯特性.此外,也研究了这些量子态二阶关联函数的四阶累积量.     

Geometrical Detection of Weak Non-Gaussianity upon Coarse-Graining

Measures of the non-Gaussianity of a random field depend on how accurately one is able to measure the field. If a signal measured at a certain point is to be averaged with its surroundings, or coarse-grained, the magnitude of its non-Gaussian component can vary. In this article, we investigate the variation of the “apparent” non-Gaussianity, as a function of the coarse-graining length, when we measure non-Gaussianity using the statistics of extrema in the field. We derive how the relative difference between maxima and minima—which is a geometrical measure of the field’s non-Gaussianity—behaves as the field is coarse-grained over increasingly larger length scales. Measuring this function can give extra information about the non-Gaussian statistics and facilitate its detection.     

Estimating Quantum Mutual Information of Continuous-Variable Quantum States by Measuring Purity and Covariance Matrix

We derive accessible upper and lower bounds for continuous-variable (CV) quantum states on quantum mutual information. The derivations are based on the observation that some functions of purities bound the difference between quantum mutual information of a quantum state and its Gaussian reference. The bounds are efficiently obtainable by measuring purities and the covariance matrix without multimode quantum state reconstruction. We extend our approach to the upper and lower bounds for the quantum total correlation of CV multimode quantum states. Furthermore, we investigate the relations of the bounds for the quantum mutual information with the bounds for the quantum conditional entropy.     

Alternative non-Gaussianity measures for quantum states based on quantum fidelity

We propose three alternative measures for non-Gaussianity of quantum states: sine distance, Bures angle, and Bures distance, which are based on quantum fidelity introduced by Wang [Phys. Lett. A 373 58 (2008)]. Using them, we evaluate the non-Gaussianity of some relevant single-mode and two-mode non-Gaussian states and find a good consistency of the three examined measures. In addition, we show that such metrics can exactly quantify the degree of Gaussianity of even Schrödinger-cat-like states of small amplitudes that can not be measured by other known non-Gaussianity measures such as the Hilbert—Schmidt metric and the relative entropy metric. We make a comparative study between all existing non-Gaussianity measures according to the metric axioms and point out that the sine distance is the best candidate among them.     

Uncertainty relation of successive measurements based on Wigner–Yanase skew information

Wigner-Yanase skew information could quantify the quantum uncertainty of the observables that are not commuting with a conserved quantity.We present the uncertainty principle for two successive projective measurements in terms of Wigner-Yanase skew information based on a single quantum system.It could capture the incompatibility of the observables,i.e.the lower bound can be nontrivial for the observables that are incompatible with the state of the quanaim system.Furthermore,the lower bound is also constrained by the quantum Fisher information.In addition,we find the complementarity relation between the uncertainties of the observable which operated on the quantum state and the other observable that performed on the post-measured quantum state and the uncertainties formed by the non-degenerate quantum observables performed on the quantum state,respectively.     

贝叶斯频率估计中频率的先验分布对有色噪声作用的影响

在贝叶斯参数估计理论框架下,研究了被测参数的先验分布对有色噪声的抑制作用.选择一个受1/f~α型谱密度有色噪声影响的自旋1/2量子比特作为量子探测系统来估计一个磁场强度的大小,利用贝叶斯代价函数的动力学演化来评判估计的精度,重点研究先验概率分布对噪声非高斯性的限制作用.研究发现:当先验概率的不确定度比较大时,有色噪声的非高斯性对频率估计精度的影响比较小;当先验概率的不确定度比较小时,有色噪声的非高斯性对频率估计精度的影响比较大.     

Quantum state tomography of an itinerant squeezed microwave field

We perform state tomography of an itinerant squeezed state of the microwave field prepared by a Josephson parametric amplifier (JPA). We use a second JPA as a preamplifier to improve the quantum efficiency of the field quadrature measurement from 2% to 36%±4%. Without correcting for the detection inefficiency we observe a minimum quadrature variance which is 68(-7)(+9)% of the variance of the vacuum. We reconstruct the state's density matrix by a maximum likelihood method and infer that the squeezed state has a minimum variance less than 40% of the vacuum, with uncertainty mostly caused by calibration systematics.     

Experimental demonstration of continuous variable quantum erasing

We experimentally demonstrate the concept of continuous variable quantum erasing. The amplitude quadrature of the signal state is labeled to another state via a quantum nondemolition interaction, leading to a large uncertainty in the determination of the phase quadrature due to the inextricable complementarity of the two observables. We show that by erasing the amplitude quadrature information we are able to recover the phase quadrature information of the signal state.     

Phase-dependent fluctuations of resonance fluorescence beyond the squeezing regime

Phase-dependent quantum features of the light scattered by a two-level atom driven by a monochromatic laser were investigated theoretically using the method of conditional homodyne detection [Carmichael, Castro-Beltran, Foster, Orozco, Phys. Rev. Lett. 85 (2000) 1855]. The splitting of fluctuations into terms of second and third order correlations of the dipole noise is obtained analytically. For the out-of-phase quadrature and weak laser driving the former are known to be squeezed. The third order fluctuations, newly found in this paper, grow with the laser intensity, contaminate squeezing below saturation, and dominate above it. They are responsible for the non-classicality and non-Gaussianity of the fluorescence for moderate to strong driving. Conditional homodyne detection, in both time and frequency domains, illustrates more general phase-dependent effects than squeezing, and is much less restricted by finite collection and quantum detector efficiencies than standard homodyne detection schemes.     

Operational quantification of continuous-variable correlations

We quantify correlations (quantum and/or classical) between two continuous-variable modes as the maximal number of correlated bits extracted via local quadrature measurements. On Gaussian states, such "bit quadrature correlations" majorize entanglement, reducing to an entanglement monotone for pure states. For non-Gaussian states, such as photonic Bell states, photon-subtracted states, and mixtures of Gaussian states, the bit correlations are shown to be a monotonic function of the negativity. This quantification yields a feasible, operational way to measure non-Gaussian entanglement in current experiments by means of direct homodyne detection, without a complete state tomography.     

Methods for Derivation of Density Matrix of Arbitrary Multi-Mode Gaussian States from Its Phase Space Representation

We present a method for derivation of the density matrix of an arbitrary multi-mode continuous variable Gaussian entangled state from its phase space representation.An explicit computer algorithm is given to reconstruct the density matrix from Gaussian covariance matrix and quadrature average values.As an example,we apply our method to the derivation of three-mode symmetric continuous variable entangled state.Our method can be used to analyze the entanglement and correlation in continuous variable quantum network with multi-mode quantum entanglement states.     

Squeezing Exchange and Entanglement between Resonantly Coupled Modes

We study the problem of squeezing exchange between two modes of the electromagnetic field modeled by quantum oscillators for the most general weak bilinear resonance coupling. Also we introduce a new measure of entanglement based on the cross covariances of the quadrature components of interacting modes. We compare the covariance measure with the measures based on the von Neumann and linear entropies of the subsystems, studying their dependences on time, coupling constants, and the initial state in the cases of parametric amplification and parametric conversion. In particular, we show that coherent states remain disentagled for all times and for any choice of coupling constants in the case of parametric converter (with accuracy up to second-order terms with respect to the strength of coupling). Also, we demonstrate that no bilinear coupling can squeeze the initial coherent state or improve the squeezing of the initial squeezed state in the case of a parametric amplifier. A strong sensitivity of the character of evolution to the choice of the set of coupling constants is discovered in the case of a parametric converter.     

Concurrence of arbitrary dimensional bipartite quantum states

We derive an analytical lower bound for the concurrence of a bipartite quantum state in arbitrary dimension. A functional relation is established relating concurrence, the Peres-Horodecki criterion, and the realignment criterion. We demonstrate that our bound is exact for some mixed quantum states. The significance of our method is illustrated by giving a quantitative evaluation of entanglement for many bound entangled states, some of which fail to be identified by the usual concurrence estimation method.     

金刚石氮空位色心耦合机械振子和腔场系统中方差压缩研究

研究了金刚石氮空位中心(NV色心)同时耦合腔场和机械振子系统中声子场的方差压缩动力学特性,分析了金刚石NV色心初态和NV色心与机械振子耦合强度对声子场方差压缩影响.结果发现:可以制备压缩时间长、压缩幅度大的声子场压缩态,其物理原因是机械振子具有最大相干性,并且通过调控NV色心初态以及磁场梯度可以实现对机械振子方差压缩非经典特性的操控,从而在理论上提供了一种调控声子场方差压缩的方式.     

Comparison between photon annihilation-then-creation and photon creation-then-annihilation thermal states:Non-classical and non-Gaussian properties

We investigate the nonclassical properties of arbitrary number photon annihilation-then-creation operation(AC) and creation-then-annihilation operation(CA) to the thermal state(TS), whose normalization factors are related to the polylogarithm function. Then we compare their quantum characters, such as photon number distribution, average photon number,Mandel Q-parameter, purity and the Wigner function. Because of the noncommutativity between the annihilation operator and the creation operator, the ACTS and the CATS have different nonclassical properties. It is found that nonclassical properties are exhibited more strongly after AC than after CA. In addition we also examine their non-Gaussianity. The result shows that the ACTS can present a slightly bigger non-Gaussianity than the CATS.     

Measurement schemes for the spin quadratures on an ensemble of atoms

We consider how to measure collective spin states of an atomic ensemble based on the multi-pass approaches for quantum interface between light and atoms. We find that a scheme with two passages of a light pulse through the atomic ensemble is efficient to implement the homodyne tomography of the spin state. Thereby, we propose to utilize optical pulses as a phase shifter that rotates the quadrature of the spins. This method substantially simplifies the geometry of experimental schemes.     

A Lower Bound of Quantum Discord for 2-Qutrit Systems

We study the lower bound of quantum discord for 2-qutrit systems. By computing the mutual information and the classical correlations of a class of states for 2-qutrit system, an analytical and computable lower bound of discord has been derived. By selecting different coefficients as examples, we can compute the lower bound of discord for 2-qutrit systems directly. The result can be generalized to the case of high-dimensional quantum state and will help us understand and explore the discord of the high-dimensional state.     

Non-classical Properties of Photon-Added Compass State

We investigate the observable non-classical features of the photon-added compass state (PACS) by its sub-Poissonian statistics, such as the Mandel’s parameter, second-order correlation function, photon-number distribution and the quasi-probability distribution functions, peculiarly the negativity in the Wigner distribution of the PACS as the specific non-classical features. We study the squeezing properties of the PACS and find the PACS does not show squeezing properties of the quadrature. Finally, we give the non-Gaussianity of the PACS by the fidelity between the PACS and the squeezed coherent state (SCS).     

基于相干叠加态的非正交编码诱骗态量子密钥分发

非正交编码协议和诱骗态方法可以有效地抵御光子数分离攻击. 由于相干叠加态中单光子成分高达90%, 常作为单光子量子比特的替代出现, 用于量子信息过程处理和计算. 本文结合非正交编码协议和诱骗态方法提出一种新的量子密钥分发方案, 光源采用相干叠加态, 推导了单光子的密钥生成速率、计数率下限和误码率的上限, 利用Matlab 模拟了无限多诱骗态情况下和有限多诱骗态情况下密钥生成速率和传输距离的关系, 得出该方案可以提升密钥生成速率并且提高安全传输距离, 验证了该方案可以进一步提高量子密钥分发系统的性能.