Harnessing Quantumness of States using Discrete Wigner Functions under (non)-Markovian Quantum Channels

The negativity of the discrete Wigner functions (DWFs) is a measure of non-classicality and is often used to quantify the degree of quantum coherence in a system. The study of Wigner negativity and its evolution under different quantum channels can provide insight into the stability and robustness of quantum states under their interaction with the environment, which is essential for developing practical quantum computing systems. The variation of DWF negativity of qubit, qutrit, and two-qubit systems under the action of (non)-Markovian random telegraph noise (RTN) and amplitude damping (AD) quantum channels is investigated. Different negative quantum states that can be used as a resource for quantum computation and quantum teleportation are constructed. The success of quantum computation and teleportation is estimated for these states under (non)-Markovian evolutions.     

Quantum phase distribution and the number—phase Wigner function of the generalized squeezed vacuum states associated with solvable quantum systems

The quantum phase properties of the generalized squeezed vacuum states associated with solvable quantum systems are studied by using the Pegg-Barnett formalism.Then,two nonclassical features,i.e.,squeezing in the number and phase operators,as well as the number-phase Wigner function of the generalized squeezed states are investigated.Due to some actual physical situations,the present approach is applied to two classes of generalized squeezed states:solvable quantum systems with discrete spectra and nonlinear squeezed states with particular nonlinear functions.Finally,the time evolution of the nonclassical properties of the considered systems has been numerically investigated.     

Wigner function of the thermo number states

Based on thermo field dynamics (TFD) and using the thermo Wigner operator in the thermo entangled state representation we derive the Wigner function of number states at finite temperature (named thermo number states). The figure of Wigner function shows that its shape gets smoothed as the temperature rises, implying that the quantum noise becomes larger.     

非Lamb-Dicke近似下制备囚禁冷离子的振动相干态

根据非Lamb-Dicke近似下激光-离子相互作用动力学规律,讨论了如何利用一系列的激光脉冲来驱动冷离子,从而从运动基态出发获得一系列振动数态的宏观叠加态.具体研究了这些叠加态的Q函数、Wigner函数和它们的非经典特性,如压缩和反群聚效应等.结果表明,合适地调节各个所用激光的脉冲长度,所产生的叠加态能很好地逼近熟知的振动相干态. 关键词： Lamb-Dicke近似 叠加态 相干态 非经典特性     

利用微脉塞重构腔场的Wigner函数

提出了重构腔场Wigner函数的一种新方案.该方案可以用微脉塞来实现.发现在腔场的Wigner函数与原子的布居数之间存在一个简单的关系.在实验上测得原子的布居数后，进行一个简单的数值积分，就可得到腔场的Wigner函数.以单光子Fock态和Schr?dinger猫态为例进行了数值模拟，发现与用精确公式计算的结果很好地相符. 关键词： 量子态重构 Wigner函数 微脉塞     

Wigner functions and tomograms of the even and odd binomial states

Using the coherent state representation of Wigner operator and the technique of integration within an ordered product (IWOP) of operators, the Wigner functions of the even and odd binomial states (EOBSs) are obtained. The physical meaning of the Wigner functions for the EOBSs is given by means of their marginal distributions. Moreover, the tomograms of the EOBSs are calculated by virtue of intermediate coordinate-momentum representation in quantum optics.     

Tunable Wigner states with dipolar atoms and molecules

We study the few-body physics of trapped atoms or molecules with electric or magnetic dipole moments aligned by an external field. Using exact numerical diagonalization appropriate for the strongly correlated regime, as well as a classical analysis, we show how Wigner localization emerges with increasing coupling strength. The Wigner states exhibit nontrivial geometries due to the anisotropy of the interaction. This leads to transitions between different Wigner states as the tilt angle of the dipoles with the confining plane is changed. Intriguingly, while the individual Wigner states are well described by a classical analysis, the transitions between different Wigner states are strongly affected by quantum statistics. This can be understood by considering the interplay between quantum-mechanical and spatial symmetry properties. Finally, we demonstrate that our results are relevant to experimentally realistic systems.     

Photon-added and photon-subtracted displaced Fock states and their non-classical properties

A new kind of quantum optical state, photon-added and -subtracted displaced Fock states, is introduced by applying the inverse of bosonic creation and annihilation operators to displaced Fock states. The quantum statistical properties of these states are investigated by numerical methods. Numerical results indicate that these states reveal some interesting non-classical properties, such as anti-bunching effects, sub-Poisson distributions and negativities of their Wigner functions.     

Quantum corrections to the entropy in a driven quantum Brownian motion model

The quantum Brownian motion model is a typical model in the study of nonequilibrium quantum thermodynamics. Entropy is one of the most fundamental physical concepts in thermodynamics.In this work, by solving the quantum Langevin equation, we study the von Neumann entropy of a particle undergoing quantum Brownian motion. We obtain the analytical expression of the time evolution of the Wigner function in terms of the initial Wigner function. The result is applied to the thermodynamic equilibrium initial state, which reproduces its classical counterpart in the high temperature limit. Based on these results, for those initial states having well-defined classical counterparts, we obtain the explicit expression of the quantum corrections to the entropy in the weak coupling limit. Moreover, we find that for the thermodynamic equilibrium initial state, all terms odd in h are exactly zero. Our results bring important insights to the understanding of entropy in open quantum systems.     

Quantum Properties of Two-Mode Squeezed Even and Odd Coherent States

Two new types of quantum states are constructed by applying the operator s(ξ) = exp(ξ*ab - ξa b ) on the two-mode even and odd coherent states.The mathematical and quantum statistical properties of such states are investigated.Various nonclassical features of these states,such as squeezing properties,the inter-mode photon bunching,and the violation of Cauchy-Schwarz inequality,are discussed.The Wigner function in these states are studied in detail.     

多输入多输出量子密钥分发信道容量研究

量子安全通信是一个量子密钥分发过程,目前采用的通信技术严重制约了量子密钥分发的比特率.将多输入多输出（MIMO）技术应用于量子密钥分发系统,可提高量子密钥分发的比特率,促进量子安全通信向高速大容量发展.文中首先构造出MIMO量子密钥分发信道中多光子纠缠态Wigner算符矩阵.并在此基础上,推导出多光子双模压缩纠缠态Wigner算符矩阵和MIMO量子密钥分发信道容量.为开发稳健的MIMO量子安全通信空时处理算法和优化设计高性能MIMO量子密钥分发系统提供理论支撑和技术基础. 关键词： 多输入多输出 双模压缩态 多光子纠缠态 信道容量     

Quantum statistical properties of photon-added spin coherent states

The photon-added spin coherent state as a new kind of coherent state has been defined by iterated actions of the proper raising operator on the ordinary spin coherent state. In this paper, the quantum statistical properties of photon-added spin coherent states such as photon number distribution, second-order correlation function and Wigner function are studied. It is found that the Wigner function shows the negativity in some regions and the second-order correlation function is less than unity. Therefore, the photon-added spin coherent state is a nonclassical state.     

Nonclassicality of photon-added squeezed vacuum states

By applying the bosonic creation operator to squeezed vacuum states, this paper introduces a new kind of quantum states: photon-added squeezed vacuum states. It also presents an experimental approach to prepare these states, and investigates their quantum statistical properties by the numerical method. The results indicate that these states reveal some interesting non-classical properties, such as anti-bunching effects, squeezing effects and negativities of the relevant Wigner functions.     

Quantum distributions for localized quantum states

The principle of ergodicity of the quantum theory has been used for elaboration of a new technique for numerical simulation of the Wigner function of open dissipative quantum systems. With this purpose the density matrix of a quantum system is represented via averaging over the ensemble of quantum states in time intervals instead of averaging over the ensemble of stochastic variables. It is shown that this approach leads to new approximate expressions for quantum distributions in the phase space, in particular, Wigner functions for systems localized in the region of classical phase trajectories. As an application, the Wigner functions are calculated for the process of intracavity second harmonic generation in the region of Hopf bifurcations.     

从离散Wigner函数的角度探讨量子相干性度量

量子相干性是量子信息处理的基本要素,在量子计算中扮演着重要的角色.为了便于讨论量子相干性在量子计算中的作用,本文从离散Wigner函数角度对量子相干性进行了探讨.首先对奇素数维量子系统的离散Wigner函数进行了分析,分离出表征相干性的部分,提出了一种可能的基于离散Wigner函数的量子相干性度量方法,并对其进行了量子相干性度量规范的分析;同时也比较了该度量与l_1范数相干性度量之间的关系.重要的是,这种度量方法能够明确给出量子相干性程度与衡量量子态量子计算加速能力的负性和之间不等式关系,由此可以解析地解释量子相干性仅是量子计算加速的必要条件.     

多光子激发相干态的Wigner函数

Wigner函数的负性是非经典量子态的重要判据之一.利用Fock态表象下Wigner函数的一般表达式,重构了相干态｜z〉的k光子激发态｜+k,z〉～a^－k｜z〉（k≥1）的Wigner函数,并根据其数值结果讨论了该量子态的非经典特性（这里a^－1为Bose湮没算符的逆算符,其作用相当于Bose产生算符）.结果表明,不论k取奇数还是偶数,相干态的这些k光子激发态都具有非经典特性;而且k的取值越大,这些量子态的非经典特性越明显. 关键词： 非经典量子态 激发相干态 Wigner函数 非经典特性     

A Wigner-function formulation of finite-state quantum mechanics

For a non-relativistic system with only continous degrees of freedom (no spin, for example), the original Wigner function can be used as an alternative to the density matrix to represent an arbitrary quantum state. Indeed, the quantum mechanics of such systems can be formulated entirely in terms of the Wigner function and other functions on phase space, with no mention of state vectors or operators. In the present paper this Wigner-function formulation is extended to systems having only a finite number of orthogonal states. The “phase space” for such a system is taken to be not continuous but discrete. In the simplest cases it can be pictured as an N×N array of points, where N is the number of orthogonal states. The Wigner function is a real function on this phase space, defined so that its properties are closely analogous to those of the original Wigner function. In this formulation, observables, like states, are represented by real functions on the discrete phase space. The complex numbers still play an important role: they appear in an essential way in the rule for forming composite systems.     

Wigner function and Bell’s inequalities for even and odd coherent states

The Wigner function and the symplectic tomogram of an entangled quantum state, which is a superposition of the photon’s coherent states (even and odd coherent states), is studied. Photon statistics and violation of Bell’s inequality for the photon state are discussed.     

Phase Properties of Photon-Added Coherent States for Nonharmonic Oscillators in a Nonlinear Kerr Medium

The potential of nonharmonic systems has several applications in the field of quantum physics. The photonadded coherent states for annharmonic oscillators in a nonlinear Kerr medium can be used to describe some quantum systems. In this paper, the phase properties of these states including number-phase Wigner distribution function,Pegg-Barnett phase distribution function, number-phase squeezing and number-phase entropic uncertainty relations are investigated. It is found that these states can be considered as the nonclassical states.