Center-of-Mass Tomography and Wigner Function for Multimode Photon States

Tomographic probability representation of multimode electromagnetic field states in the scheme of center-of-mass tomography is reviewed. Both connection of the field state Wigner function and observable Weyl symbols with the center-of-mass tomograms as well as connection of the Grönewold kernel with the center-of-mass tomographic kernel determining the noncommutative product of the tomograms are obtained. The dual center-of-mass tomogram of the photon states are constructed and the dual tomographic kernel is obtained. The models of other generalized center-of-mass tomographies are discussed. Example of two-mode even and odd Schrödinger cat states is presented in details.     

Wigner Functions and Spin Tomograms for Qubit States

We establish the relation of the spin tomogram to the Wigner function on a discrete phase space of qubits. We use the quantizers and dequantizers of the spin tomographic star-product scheme for qubits to derive the expression for the kernel connecting Wigner symbols on the discrete phase space with the tomographic symbols.     

奇偶对相干态的维格纳函数和层析图函数

利用纠缠态η〉表象下的维格纳算符,重构了奇偶对相干态的维格纳函数.根据维格纳函数在相空间中随变量ρ和γ的变化规律,讨论了奇偶对相干态的非经典性质和量子干涉效应.研究发现,奇偶对相干态总呈现非经典性质,并且当q取奇数时,奇偶对相干态更容易出现非经典性质.奇偶对相干态的量子干涉效应的显著程度与q取值有关,但对于q的同一取值,奇对相干态的量子干涉效应更为显著.利用纠缠态η〉表象下的维格纳算符Δ1,2(ρ,γ)和纠缠态η,τ1,τ2〉的投影算符之间满足的拉东变换,获得了奇偶对相干态的量子层析图函数.     

双模激发压缩真空态的维格纳函数

利用纠缠态表象下的维格纳(Wigner)算符,构造了双模激发压缩真空态的维格纳函数,并根据该函数在相空间ρ-γ中随参量m,n和r的变化关系,讨论了双模激发压缩真空态的量子干涉特性和压缩效应。结果表明,对于参量m,n不同的取值,双模激发压缩真空态的量子干涉效应的强弱不同;而对于不同的压缩参量r,双模激发压缩真空态呈现出不同程度的压缩效应。最后,根据双模激发压缩真空态的维格纳函数的边缘分布,阐明了此维格纳函数的物理意义。     

Wigner Functions for Two-Variable Hermite Polynomial States and Their Time-Evolutions Under Thermal Environment

We analytically study the Wigner function (WF) for the two-variable Hermite polynomial state (TVHPS) and the effect of decoherence on the TVHPS in thermal environment. The nonclassicality of the TVHPS is investigated in terms of the partial negativity of the WF which depends on the polynomial orders m,n and the squeezing parameter r. We also investigate how the WF for the TVHPS evolves in the thermal environment. At long times, the TVHPS decays to thermal, a mixed Gaussian state, within the thermal environment.     

Generalized Wigner Operator and Bivariate Normal Distribution in p-q Phase Space

We introduce a kind of generalized Wigner operator, whose normally ordered form can lead to the bivariate normal distribution in p-q phase space. While this bivariate normal distribution corresponds to the pure vacuum state in the generalized Wigner function phase space, it corresponds to a mixed state in the usual Wigner function phase space.     

Wigner Functions and Tomograms of the Even and Odd Negative 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 negative binomial states (NBSs) are obtained. We concentrate our analysis on the fact that the even and odd NBSs interpolate between the even and odd coherent states and the even and odd quasi-thermal states depending on the values of the parameters involved. Moreover, the tomograms of the even and odd NBSs are calculated by virtue of intermediate coordinate-momentum representation in quantum optics. Project 10574060 supported by the National Natural Science Foundation of China and project Q2007A01 supported by the Natural Science Foundation of Shandong Province.     

Entropy and Wigner Distribution Functions Revisited

Several expressions for quantum entropy proposed in the literature are evaluated within the Weyl—Wigner—Moyal phase-space representation of quantum mechanics, with emphasis on some important subtle points in this approach. It has been found that the Rényi—Süßmann entropy and its linearization are distinguished because of their properties.     

任意两个相干态的叠加态的相位分布和Wigner函数(英文)

从相位分布和Wigner函数两个方面研究了任意两个相干态|β〉and |mβeiδ〉的叠加态的量子统计性质.结果表明这种叠加态的非经典特性与β2,振幅系数m,相干态间的位相差δ以及叠加系数间的位相差都有关.当参量选择合适,这种叠加态存在着量子效应.计算了两个相干态等几率混合系综的相位分布和Wigner函数,经过与前者比较,结果表明由于相干项的存在,使得叠加态具有很好的量子力学行为.     

Mutual Restriction between Concurrence and Intrinsic Concurrence for Arbitrary Two-Qubit States

Concurrence is viewed as the most commonly approach for quantifying entanglement of two-qubit states, while intrinsic concurrence contains concurrence of four pure states consisting of a special pure state ensemble concerning an arbitrary two-qubit state. Thus, a natural question arises: Whether there is a specified relation between them.We firstly examine the relation between concurrence and intrinsic concurrence for the maximally nonlocal mixed state under a special unitary operation, which is...     

Entanglement Dynamics and Transfer for Two-Qubit Werner-Like States in Markovian Environments

We investigate entanglement dynamics and transfer in a system of two identical independent qubits, each of them locally interacting with a bosonic reservoir. Starting from two-qubit extended Werner-like states, we have shown that the degree of entanglement of the initial states, Markovian environments and the purity can control the time of the two-qubit entanglement sudden death and the reservoirs’ entanglement sudden birth. Moreover, the phenomenon of entanglement sudden death/birth may occur depending on the values of parameters like purity or degree of entanglement of the initial state. When initial states are not pure, entanglement sudden death/birth always occurs, this will permit us to link the occurrence time of entanglement sudden death/birth and entanglement transfer to the purity or the degree of entanglement of the initial states.     

Modified Form of Wigner Functions for Non-Hamiltonian Systems

Quantization of non-Hamiltonian systems （such as damped systems） often gives rise to complex spectra and corresponding resonant states, therefore a standard form calculating Wigner functions cannot lead to static quasiprobability distribution functions. We show that a modified form of the Wigner functions satisfies a ＊-genvalue equation and can be derived from deformation quantization for such systems.     

Semiclassical States Associated with Isotropic Submanifolds of Phase Space

We define classes of quantum states associated with isotropic submanifolds of cotangent bundles. The classes are stable under the action of semiclassical pseudo-differential operators and covariant under the action of semiclassical Fourier integral operators. We develop a symbol calculus for them; the symbols are symplectic spinors. We outline various applications.     

Generalized Wigner Functions for Damped Systems in Deformation Quantization

Quantization of damped systems usually gives rise to complex spectra and corresponding resonant states, which do not belong to the Hilbert space. Therefore, the standard form of calculating Wigner function (WF) does not work for these systems. In this paper we show that in order to let WF satisfy a *-genvalue equation for the damped systems, one must modify its standard form slightly, and this modification exactly coincides with the resu lts derived from a *-Exponential expansion in deformation quantization.     

Interference in Phase Space of Squeezed States for the Time-Dependent Hamiltonian System

We showed that the idea of Schleich and Wheeler (1987, Nature 326, 574) for the semiclassical approach of the interference in phase space of harmonic oscillator squeezed states can be extended to that of general time-dependent Hamiltonian system. The quantum phase properties of squeezed states for the general time-dependent Hamiltonian system are investigated by using the quantum distribution function. The weighted overlaps A _n and phases θ _n for the system are evaluated in the semiclassical limit.     

Efficient Schemes of Joint Remote State Preparation for Two-Qubit Equatorial States

Recently, Binayak S. Choudhury (Quantum Inf. Process 13, 239 2014), proposed a protocol of joint remote state preparation of an equatorial two-qubit pure quantum state using GHZ states. According to their scheme the probability of success is 0.25. In this letter, an improved scheme is proposed, which can enhance the probability of success to 100 %. Moreover, we propose a scheme to prepare the two-qubit pure quantum state whose coefficient is more general.     

Scalar Charged Particle in Weyl–Wigner–Moyal Phase Space. Constant Magnetic Field

A relativistic phase-space representation for a class of observables with matrix-valued Weyl symbols proportional to the identity matrix (charge-invariant observables) is proposed. We take into account the nontrivial charge structure of the position and momentum operators. The evolution equation coincides with its analog in relativistic quantum mechanics with nonlocal Hamiltonian under conditions where particle-pair creation does not take place (free particle and constant magnetic field). The differences in the equations are connected with the peculiarities of the constraints on the initial conditions. An effective increase in coherence between eigenstates of the Hamiltonian is found and possibilities of its experimental observation are discussed.     

New Maximally Entangled States and Pattern Classification in Two-Qubit System

Pattern classifications have been performed by employing the method of Grover’s iteration on Bell’s MES and Singh-Rajput MES in two-qubit system and it has been demonstrated that for any pattern classification in a two-qubit system the maximally entangled states of Singh-Rajput eigen basis provide the most suitable choice of search states while in no case any of Bell’s states is suitable for such pattern classifications.