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We prove semiclassical estimates for the Schrödinger-von Neumann evolution with C 1 , 1 potentials and density matrices whose square root have either Wigner functions with low regularity independent of the dimension, or matrix elements between Hermite functions having long range decay. The estimates are settled in different weak topologies and apply to initial density operators whose square root have Wigner functions 7 times differentiable, independently of the dimension. They also apply to the N -body quantum dynamics uniformly in N and to concentrating pure and mixed states without any regularity assumption. In a appendix, we finally estimate the dependence in the dimension of the constant appearing on the Calderón-Vaillancourt Theorem. [ABSTRACT FROM AUTHOR]

We explore into the non-classical characteristics of a new entangled coherent state (CS), also known as a multi-photon addition amplified coherent state (MPAACS) g n ̂ a ̂ † m , which is produced by adding any quantity of photons to two-mode coherent states with various gain factor values. A superposition of photon-added amplified two-mode CSs (MPAACS) also exists in this novel entangled state. It is proven that the gain factor and Laguerre polynomials are related to the MPAACS normalization factor. Analytical discussion is also had regarding entanglement and quantum statistical properties. Regarding concurrence, our findings further suggest that by selecting suitable values for the gain factor g , photon added (m , n) , and coherent amplitude, entanglement for the output state can occur. Specifically, the enhancement of the entanglement can be found at large g values at fixed (m , n) in comparison to (m , n) values at fixed g and small amplitude with ϕ = 0 or pi. Besides that, the analyses of nonclassicality reveal that, when comparing the results for several values (m , n) at fixed g and with several values g at fixed (m , n) , the low-order antibunching effect, the cross-correlation function, and the Wigner function all support the sub-Poissonian statistics. When analyses of the nonclassicality and the negative value of the WF for ϕ = 0 are larger at fixed parameter (m , n) , but larger at g fixed for ϕ = π , the TMAA-TMC states perform better. [ABSTRACT FROM AUTHOR]

Experimental realization of various quantum states of interest has become possible in the recent past due to the rapid developments in the field of quantum state engineering. Nonclassical properties of such states have led to various exciting applications, specifically in the area of quantum information processing. The present article aims to study lower- and higher-order nonclassical features of such an engineered quantum state (a generalized binomial state based on Abel's formula). Present study has revealed that the state studied here is highly nonclassical. Specifically, higher-order nonclassical properties of this state are reported using a set of witnesses, like higher-order antibunching, higher-order sub-Poissonian photon statistics, higher-order squeezing (both Hong–Mandel type and Hillery type). A set of other witnesses for lower- and higher-order nonclassicality (e.g., Vogel's criterion and Agarwal's A parameter) have also been explored. Further, an analytic expression for the Wigner function of the generalized binomial state is reported and the same is used to witness nonclassicality and to quantify the amount of nonclassicality present in the system by computing the nonclassical volume (volume of the negative part of the Wigner function). Optical tomogram of the generalized binomial state is also computed for various conditions as Wigner function cannot be measured directly in an experiment in general, but the same can be obtained from the optical tomogram with the help of Radon transform. [ABSTRACT FROM AUTHOR]

We construct some orthogonal states for single-mode squeezed vacuum state (SVS) and study their nonclassicality by virtue of the quadrature squeezing and the Wigner function. The orthogonalizer is based on the photon-addition operation, i.e., the repeated (m times) application of the photon creation operator. The orthogonal state and the photon-addition single-mode SVS are same for odd m but different for even m. The squeezing effect of the orthogonal states will exhibit when the origin squeezing parameter is greater than a certain value. Moreover, the negativity of the Wigner function shows their nonclassicality. [ABSTRACT FROM AUTHOR]

Abstract We investigate nonclassical properties of the quantum state generated by adding any number of photons to the two-mode coherent states. This novel quantum state is also a superposition of photon-added two-mode CSs (PATMCS). It is shown that the normalization factor of the PATMCS is related to the Laguerre polynomials. The quantum statistical properties, squeezing effects, entanglement and nonlocality are also discussed analytically. Our results show that the PATMCS is a new nonclassical, squeezing and entangled state with negative Wigner function, negative quadrature squeezing and violation of the Bell-CHSH inequality. [ABSTRACT FROM AUTHOR]

In this paper, we use the displacement operator together with parity operation to construct the superposition of two coherent states. By transmitting this superposition from 50–50 beam splitter the two-mode qubit-like entangled coherent state (ECS) is generated. Moreover, we introduce a controllable method for producing qutrit-like ECS using atom–field interaction in cavity QED and beam splitter. We will show that the distances of peaks of Wigner functions for reduced density matrices of two-mode ECS's are entanglement sensitive and can be witnesses of entanglement. To confirm the results we use concurrence measure to compare bipartite entanglement of ECS's with the behaviour of peaks of Wigner functions. Moreover, we investigate decoherence effects on Wigner function, arising from transmitting ECS's through noisy channels. [ABSTRACT FROM AUTHOR]

The Lorentz-Abraham-Dirac differential motion equation is of the third order since it contains the second order acceleration v → ¨ , which stands for the radiation friction force. To achieve a rigorous and comprehensive assessment of the dynamics of such radiation-friction systems it is necessary to expand the phase space { r → , v → } and to introduce higher kinematic values, such as v → ˙ and v → ¨. Our study is dedicated to the problem of building of an expanded phase space { r → , v → , v → ˙ , v → ¨ } , within which the fourth Vlasov equation for the distribution function f (r → , v → , v → ˙ , v → ¨ , t) is considered. Since the second Vlasov equation for the distribution function f (r → , v → , t) in a particular case is shown to transform into the Moyal equation for the Wigner function W (r → , p → , t) , the authors have elaborated and present a way to expand the Wigner function on the phase space { r → , v → , v → ˙ , v → ¨ } and also propose a new Moyal equation, which this function satisfies. • The Wigner function W (r → , p → , p → ˙ , p → ¨ , t) of the 4th rank for the phase space { r → , p → , p → ˙ , p → ¨ } is obtained. • The new extended Moyal equation for the Wigner function W (r → , p → , p → ˙ , p → ¨ , t) is obtained. • The method for finding the exact solution of the third Vlasov equation is proposed. [ABSTRACT FROM AUTHOR]

Abstract Squeezed states are one of the most useful quantum optical models having various applications in different areas, especially in quantum information processing. Generalized squeezed states are even more interesting since, sometimes, they provide additional degrees of freedom in the system. However, they are very difficult to construct and, therefore, people explore such states for individual setting and, thus, a generic analytical expression for generalized squeezed states is yet inadequate in the literature. In this article, we propose a method for the generalization of such states, which can be utilized to construct the squeezed states for any kind of quantum models. Our protocol works accurately for the case of the trigonometric Rosen–Morse potential, which we have considered as an example. Presumably, the scheme should also work for any other quantum mechanical model. In order to verify our results, we have studied the nonclassicality of the given system using several standard mechanisms. Among them, the Wigner function turns out to be the most challenging from the computational point of view. We, thus, also explore a generalization of the Wigner function and indicate how to compute it for a general system like the trigonometric Rosen–Morse potential with a reduced computation time. Highlights • A scheme for generalization for the squeezed states has been explored. • An exact analytical expression of the generalized squeezed states has been provided. • Several nonclassical properties of the constructed state have been analyzed. • Generalized expression of squeezed states has been employed to a particular example, namely the Rosen–Morse potential. • In all perspective, we have found a consistent behavior of the generalized squeezed states. [ABSTRACT FROM AUTHOR]

We study the ionization of an H atom in a linearly polarized laser field with different optical cycle numbers by calculating the entangled trajectories in phase space. The results indicate that, for a two-cycle laser pulse, the entangled trajectory is simple owing to the simple laser electric distribution. As the number of optical cycles increases, the complexity of the laser electric field distribution, and subsequently, that of the entangled trajectories increase. From these entangled trajectories, re-scattering ionization can be observed. Further, we investigate the effect of quantum force on trajectories by comparing them with classical trajectories. We find that for few-cycle laser pulses ( n p = 2 and 4), the effect of the quantum force is more distinct than classical behavior, whereas for longer laser pulses ( n p = 6 and 8), it is quite similar to the classical behavior. Because of the quantum force, the final kinetic energy is slightly higher than that obtained by classical calculation. The different initial positions have some influence on the individual trajectories, but the individual trajectories still keep similar configuration to the mean trajectories. [ABSTRACT FROM AUTHOR]

We define a new quantifier of classicality for a quantum state, the Roughness, which is given by the L 2 ( R 2 ) distance between Wigner and Husimi functions. We show that the Roughness is bounded and therefore it is a useful tool for comparison between different quantum states for single bosonic systems. The state classification via the Roughness is not binary, but rather it is continuous in the interval [ 0 , 1 ] , being the state more classic as the Roughness approaches to zero, and more quantum when it is closer to the unity. The Roughness is maximum for Fock states when its number of photons is arbitrarily large, and also for squeezed states at the maximum compression limit. On the other hand, the Roughness approaches its minimum value for thermal states at infinite temperature and, more generally, for infinite entropy states. The Roughness of a coherent state is slightly below one half, so we may say that it is more a classical state than a quantum one. Another important result is that the Roughness performs well for discriminating both pure and mixed states. Since the Roughness measures the inherent quantumness of a state, we propose another function, the Dynamic Distance Measure (DDM), which is suitable for measure how much quantum is a dynamics. Using DDM, we studied the quartic oscillator, and we observed that there is a certain complementarity between dynamics and state, i.e. when dynamics becomes more quantum, the Roughness of the state decreases, while the Roughness grows as the dynamics becomes less quantum. [ABSTRACT FROM AUTHOR]

In this paper, we investigate how a m -photon enhanced chaotic field (PACF), denoted by 1 − e − λ m + 1 a † m e − λ a † a a m / m !, evolves in an amplitude damping channel with a damping constant κ . By using the technique of integration within ordered product of operators (IWOP), we find that it evolves into a Laguerre function-weighted chaotic field which is described by ⋮ e 1 − e λ e 2 κ t aa † L m e λ + 2 κ t aa † ⋮ , which is in antinormal ordering. Time evolution of photon number average and fluctuation in this process are also derived. The corresponding evolution law of the Wigner function is also deduced analytically. [ABSTRACT FROM AUTHOR]

In this paper, we show that by partial tracing the pure state in higher dimension one can deduce the mixed state of light field. In this paper the pure state in higher dimension is a three-mode squeezed state S 23 σ S 31 τ 000 000 S 31 − 1 τ S 23 − 1 σ , while the mixed state's density operator is sec h 2 σ sec h 2 τ e a 2 † a 3 † tanh σ sec h 2 σ tanh 2 τ a 3 † a 3 0 22 0 e a 2 a 3 tanh σ , which involves both squeezing and chaotic properties of optical field. We further explain how such kind of light field can be generated by passing a two-mode squeezed light though a single-mode dissipative channel, its Wigner function is discussed by using the coherent state representation. Our work provides an important method, which can be used to theoretically find more optical fields in quantum communication and quantum optics. [ABSTRACT FROM AUTHOR]

Nonclassical properties of photon added and subtracted squeezed coherent states have been compared with specific focus on the higher-order nonclassicalities, such as higher-order squeezing, higher-order sub-Poissonian photon statistics, higher-order antibunching. It is observed that both photon added and subtracted squeezed coherent states are highly nonclassical as they satisfy criteria for all of the above mentioned nonclassicalities and a set of other criteria including negativity of Wigner function, Klyshko's criterion and Agarwal's ( A 3 ) parameter. Further, the amount of nonclassicality present in these two types of states has been compared quantitatively using a measure of nonclassicality known as nonclassical volume. Variation in the amount of nonclassicality with the number of photon(s) added/subtracted is also investigated, and it is found that the addition of photons makes the squeezed coherent state more nonclassical than what is done by the subtraction of photons. [ABSTRACT FROM AUTHOR]

We proposed a theoretical scheme for generating a new kind of non-Gaussian state—Hermite polynomial excited squeezed vacuum states—by using parametric amplifier process and conditional measurement. Specially, two different single-mode squeezed vacuum states were injected into the signal and idler ports of parametric amplifier and m -photon was detected in idler output port, then the new non-Gaussian state is generated in signal port. It's normalization factor is found to be related with Legendre polynomials that corresponds to the success probability of such event. We investigated the nonclassical properties according to photon-number distribution, sub-Poissonian distribution, anti-bunching effect, quadrature squeezing effect, and Wigner function. It is shown that there is a wide range of nonclassical phenomena created by tuning the interaction parameters. Our study may provide a theoretical reference to generate nonclassical state for experiment. [ABSTRACT FROM AUTHOR]

A theoretical scheme is proposed to generate an asymmetrical entangled coherent state from two separate coherent state by similar quantum-optical catalysis. We give the explicit expression of the generated state and discuss its success probability. Some nonclassical properties such as antibunching effect and the negativity of the Wigner function, are studied in detail. [ABSTRACT FROM AUTHOR]

Symplectic quantum mechanics (SMQ) makes possible to derive the Wigner function without the use of the Liouville–von Neumann equation. In this formulation of the quantum theory the Galilei Lie algebra is constructed using the Weyl (or star) product with Q ˆ = q ⋆ = q + i ħ 2 ∂ p , P ˆ = p ⋆ = p − i ħ 2 ∂ q , and the Schrödinger equation is rewritten in phase space; in consequence physical applications involving the Coulomb potential present some specific difficulties. Within this context, in order to treat the Schrödinger equation in phase space, a procedure based on the Levi-Civita (or Bohlin) transformation is presented and applied to two-dimensional (2D) hydrogen atom. Amplitudes of probability in phase space and the correspondent Wigner quasi-distribution functions are derived and discussed. [ABSTRACT FROM AUTHOR]

A non-Gaussian state being a mixture of the vacuum and single-photon states can be generated by truncating a thermal state in a quantum-scissors device of Pegg et al. (1998) [12] . In contrast to the thermal state, the generated state shows nonclassical property including the negativity of Wigner function. Besides, signal amplification and signal-to-noise ratio enhancement can be achieved. [ABSTRACT FROM AUTHOR]

A differential formalism for the covariance matrix of thermal equilibrium states is obtained when the Hamiltonian of the system is defined by quadratic forms. First, the cases of one- and two-modal Gaussian states are taken into account and the differential equations for the corresponding covariance matrices of these states in terms of the temperature are obtained. Later, the generalization of the differential equation to any number of modes is demonstrated by using the Wigner quasi-probability distribution. Some examples related to standard quadratic Hamiltonians are given and several thermodynamic properties as the free and internal energies, the entropy, and the heat capacity of different systems are listed. • A differential formalism for the covariance matrix of Gaussian thermal equilibrium states is obtained. • The formalism is generalized for any number of modes and quadratic Hamiltonians. • A general solution is proposed and its applicability is mentioned. • The frequency converter and parametric amplifier thermal states solutions are obtained explicitly. • Different thermodynamic quantities are calculated and discussed. [ABSTRACT FROM AUTHOR]

Based on the one- and two-mode combinatorial squeezed state (H.Y. Fan, Phys. Rev. A. 41(3), 1526 (1990))which can enhance squeezing effect, we derive a new optical field by using partial tracing method, we not only obtain its density operator but also deduce its Wigner function by virtue of operators' Weyl ordering property. This new photon field possesses more photon numbers than the corresponding chaotic field, and can be applied to quantum controlling and quantum information processing. [ABSTRACT FROM AUTHOR]

We study the entanglement evolution of a quantum optical vortex state propagating through coupled lossless waveguides. We consider states generated by coupling two squeezed modes using a sequence of beam splitters and also by subtracting photons from one of the output modes in spontaneous parametric down conversion. We use the Wigner function to study the variation in the structure of the vortex state with distance and quantify the entanglement after propagation using logarithmic negativity . [ABSTRACT FROM AUTHOR]

Squeezed state of light is one of the important subjects in quantum optics which is generated by optical nonlinear interactions. In this paper, we especially focus on qubit like entangled squeezed states (ESS's) generated by beam splitters, phase-shifter and cross Kerr nonlinearity. Moreover the Wigner function of two-mode qubit and qutrit like ESS are investigated. We will show that the distances of peaks of Wigner functions for two-mode ESS are entanglement sensitive and can be a witness for entanglement. Like the qubit cases, monogamy inequality is fulfilled for qutrit like ESS. These trends are compared with those obtained for qubit and qutrit like entangled coherent states (ECS). [ABSTRACT FROM AUTHOR]

We theoretically generate single-photon catalyzed coherent states (SPCCSs) by means of quantum-optical catalysis based on the beam splitter (BS) or the parametric amplifier (PA). These states are obtained in one of the BS (or PA) output channels if a coherent state and a single-photon Fock state are present in two input ports and a single photon is registered in the other output port. The success probabilities of the detection (also the normalization factors) are discussed, which is different for BS and PA catalysis. In addition, we prove that the generated states catalyzed by BS and PA devices are actually the same quantum states after analyzing photon number distribution of the SPCCSs. The quantum properties of the SPCCSs, such as sub-Poissonian distribution, anti-bunching effect, quadrature squeezing effect, and the negativity of the Wigner function are investigated in detail. The results show that the SPCCSs are non-Gaussian states with an abundance of nonclassicality. [ABSTRACT FROM AUTHOR]

We consider an optomechanical system with two membranes when a bichromatic laser field with red-sideband and blue-sideband frequencies is applied in the single photon strong coupling regime. It is shown that using the mode selecting method and under the Lamb–Dicke approximation, motion of membranes can evolve to single or two mode squeezed number states. By considering the environmental effect, a Wigner function is plotted for understanding the conditions that lead to the generation of non-Gaussian states. The results show that, in this system, initial states of membranes are important to generation of non-Gaussian mechanical squeezed number states. [ABSTRACT FROM AUTHOR]

The nonlinear interaction between an optical field and a mechanical resonator of an opto-mechanical system plays an important role in quantum optics and quantum information. This work applies the nonlinearity of opto-mechanical system to generate a nonclassical state for an initial state composed of four-headed cat state of photonic mode and number state of mechanical mode. It is interesting to find that the Wigner function of a mechanical mode is composed of finite Wigner functions of time-dependent displaced number states, which is very useful in quantum information process. Furthermore, nonclassical properties of the photonic and mechanical modes are investigated by using Wigner function. An interesting result is that the negative volume of Wigner function for the photonic (or mechanical) mode increases with parameter α (or k ), which means that the larger initial value of photonic (or mechanical) mode will improve the nonclassicality of the photonic (or mechanical) mode. We also investigate the influence of different initial photonic states on the nonclassicality of mechanical and photonic modes. [ABSTRACT FROM AUTHOR]

Gaussian state decoherence aspects due to interacting magnetic-like and gravitational fields are quantified through the quantum fidelity and Shannon entropy in the scope of the phase-space representation of elementary quantum systems. For Gaussian Wigner functions describing harmonic oscillator states, an interacting external field destroys the quantum fidelity and introduces a quantum beating behavior. Likewise, it introduces harmonic profiles for free particle systems. Some aspects of quantum decoherence for the quantum harmonic oscillator and for the free particle limit are also quantified through the Shannon entropy. For the gravitational quantum well, the effect of a magnetic-like field on the quantum fidelity is suppressed by the linear term of the gravitational potential. To conclude, one identifies a fine formal connection of the quantum decoherence aspects discussed here with the noncommutative quantum mechanics. [ABSTRACT FROM AUTHOR]

A projection synthesis scheme for generating Hermite polynomial excited squeezed vacuum states (HPESVSs, non-Gaussian quantum states) is proposed. Injecting two separate single-mode squeezed vacuum states into a beam splitter and counting the photons in one of the output channels (conditional measurement or post-detection), the conditional state in the other channel is just the HPESVS. The success probability, related to a Legendre polynomial form, is obtained analytically and analyzed numerically in detail. To exhibit the nonclassical effects of this conditional state, we also present the photon-number distribution, sub-Poissionian distribution, anti-bunching effect, quadrature squeezing effect, and Wigner function, respectively. The results show that by tuning the interaction parameters, a wide range of nonclassical phenomena can be created. [ABSTRACT FROM AUTHOR]

Many novel quantum phenomena emerge in non-equilibrium relativistic quantum matter under extreme conditions such as strong magnetic fields and rotations. The quantum kinetic theory based on Wigner functions in quantum field theory provides a powerful and effective microscopic description of these quantum phenomena. In this article we review some of recent advances in the quantum kinetic theory and its applications in describing these quantum phenomena. [ABSTRACT FROM AUTHOR]

We investigate the effect of uncertainty principle on the simulation of quantum transport based on the Wigner function. We show that due to the positional uncertainty of electrons within the device, which bounds the region for nonlocal potential correlation, a constraint is imposed via the uncertainty principle on the possible momentum resolution of the Wigner function. It is numerically demonstrated that its violation deteriorates the simulation results significantly in configurations where the quantum effects are crucial. [ABSTRACT FROM AUTHOR]

We study a class of phase-space distribution functions that is generated from a Gaussian convolution of the Wigner distribution function. This class of functions represents the joint count probability in simultaneous measurements of position and momentum. We show that, using these functions, one can determine the expectation value of a certain class of operators accurately, even if measurement data performed only with imperfect detectors are available. As an illustration, we consider the eight-port homodyne detection experiment that performs simultaneous measurements of two quadrature amplitudes of a radiation field. [ABSTRACT FROM AUTHOR]

We theoretically examine nonclassical properties of the field states generated by repeatedly applying photon annihilation-then-creation operation (AC) and creation-then-annihilation operation (CA) to the squeezed vacuum (SV). We firstly derive their normalization factors and then compare their statistical properties, such as photon number distribution, mean photon number, Mandel Q parameter, and the Wigner function. It is found that the ACSV can present more clear nonclassicality than the CASV. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the connection between two alternative descriptions of the quantum motion proposed by Wigner in 1932 and by Bohm in 1952. Such formalism provides different representations of the quantum dynamics. The Wigner description is based on the definition of a non positive quasi-distribution function in the quantum phase space and the Bohm formalism on the introduction of the pilot wave field associated to the particle motion along trajectories. We discuss the representation of the Bohm dynamics in the phase space in terms of a suitable Wigner measure. We propose an extension of the Wigner transformation and we derive a family of models where the quantum dynamics is described by equivalent mathematical formulations. Similarly to the classical limit, we show the asymptotic convergence in distributional sense of the extended Wigner distribution to a measure. We prove that such a limit is the solution of a classical Liouville equation containing as a quantum correction the Bohm potential. • Quantum properties of atoms impact the electronic structure of nanomaterials. • Alternative interpretations of quantum mechanics have found renewed interest. • Mathematical link between the Wigner phase space motion and the Bohm dynamics. • Classical-to-quantum transition understood in terms of motion in phase space. [ABSTRACT FROM AUTHOR]

For a quantum oscillator with the polynomial potential an explicit expression that describes the energy distribution as a coordinate (and momentum) function is obtained. The presence of the energy function poles is shown for the quantum system in the domains where the Wigner function has negative values. [ABSTRACT FROM AUTHOR]

Quantum scissors devices proposed by Pegg are beneficial to obtain highly nonclassical quantum states and indispensable for meeting the requirements of quantum information and computation. In this paper, via inputting and detecting single photon states, quantum scissor operation is equivalent to a mixed superposition of three pure state projection operators, which means that the output states are always truncated for any input state. We theoretically prepare a class of non-Gaussian quantum states via thermal state truncation and investigate their statistical properties using average photon number, gain intensity and signal to noise ratio. It is shown that the intensity gain and signal to noise ratio greater than one can be achieved by modulating the thermal parameter and the transmissivity, which realizes the signal amplification and enhancement. Besides, quantum scissor operation can generate the highly non-classical quantum state by investigating the negativity volume of Wigner function. These results indicate that the usage of the new non-Gaussian states may have potential applications in certain quantum information processing. • A new quantum scissors device is designed and used to truncate the thermal state. • Signal amplification and enhancement can be realized. • Highly nonclassicality can be created via the negativity of Wigner function. [ABSTRACT FROM AUTHOR]

The negativity of the Wigner function is discussed as a measure of the non-classicality and the quantum interference pattern obtained therein as a possible measure of the entanglement between the two modes of the vortex states. This measure of entanglement is compared with the results obtained from concurrence. [ABSTRACT FROM AUTHOR]

We introduce a new method to calculate the Wigner function when its corresponding Husimi function is given. A new formula is derived for calculating conveniently the Wigner function in two-mode entangled state representation. As application, we derive Wigner functions of some quantum states, such as two-mode entangled state, the electron's two-mode squeezed canonical coherent state, and the electron's coordinate eigenstate. [ABSTRACT FROM AUTHOR]

A new kind of non-Gaussian quantum state is constructed by operating the superposed operator (SO) (cosθaa†+sinθa†a) on a squeezed vacuum state (SVS) S(r)|0〉. It is found that the SOSVS is just a superposition state between S(r)|0〉 and S(r)|2〉 with only even numbers of photons. The nonclassicality is investigated by exploring the negativity of Wigner function (WF) and the sub-Poissonian distribution of Mandel's Q-parameter. The non-Guassianity is exhibited via the fidelity between the SOSVS and the SVS and the marginal distribution of its Wigner function. It is found that such SO on the SVS can enhance the nonclassicality and change the non-Gaussianity of the SOSVS. This provides the possibility of generating quantum states with specific nonclassical and non-Gaussian properties. [ABSTRACT FROM AUTHOR]

In this paper, we give a detailed derivation process for the Wigner function (WF) of an arbitrary photon-catalyzed optical coherent state (APCOCS), which can be generated via interference between coherent and Fock states using quantum catalysis. We find that the WF is non-Gaussian and is related to the two-variable Hermite polynomial of the relative parameters, such as the coherent field strength, the number of catalyst photons and the control ratio of the beam splitter. It showed that the APCOCS created a wide range of nonclassical properties. [ABSTRACT FROM AUTHOR]

Abstract: We investigate nonclassical properties of the optical field when photon subtraction and addition coherent operation acts on an odd superpositions of coherent states (SCSs) by examining its sub-Poissonian statistics, quadrature squeezing, and negativity of the Wigner function (WF). It is found that these nonclassical properties can be all significantly enhanced for the output state when the coherent operation is applied to an odd SCSs. Moreover, the results show that the nonclassicality of the coherent operation of SCSs (COSCSs) is sensitive to the coherent operation and amplitude. [Copyright &y& Elsevier]

Abstract: There are quantum states of light that can be expressed as finite superpositions of Fock states (FSFS). We demonstrate the nonclassicality of an arbitrary FSFS by means of its phase space distributions such as the Wigner function and the Q-function. The decoherence of the FSFS is studied by considering the time evolution of its Wigner function in amplitude decay and phase damping channels. As examples, we determine the nonclassicality and decoherence of generalized and reciprocal binomial states. [Copyright &y& Elsevier]

• The Wigner distribution and the tomographic representation associated to cyclic states and dihedral states are obtained. • The pseudo-probability and probability functions are obtained for superpositions of Gaussian states in the phase space. • The characteristics of the tomogram are discussed from the point of view of the quantizer-dequantizer formalism. • The resulting Wigner and optical tomograms are show for several examples and their properties are discussed. • The Wigner function presents non-classical behavior. Within the framework of the probability representation of quantum mechanics, we study a superposition of generic Gaussian states associated to symmetries of a regular polygon of n sides; in other words, the cyclic groups (containing the rotational symmetries) and dihedral groups (containing the rotational and inversion symmetries). We obtain the Wigner functions and tomographic probability distributions (symplectic and optical tomograms) determining the density matrices of the states explicitly as the sums of Gaussian terms. The obtained Wigner functions demonstrate nonclassical behavior, i.e., contain negative values, while the tomograms show a series of maxima and minima different for each state, where the number of the critical points reflects the order of the group defining the states. We discuss general properties of such a generalization of normal probability distributions. [ABSTRACT FROM AUTHOR]

Abstract: We analyze the tunneling of a particle through a repulsive potential resulting from an inverted harmonic oscillator in the quantum mechanical phase space described by the Wigner function. In particular, we solve the partial differential equations in phase space determining the Wigner function of an energy eigenstate of the inverted oscillator. The reflection or transmission coefficients R or T are then given by the total weight of all classical phase-space trajectories corresponding to energies below, or above the top of the barrier given by the Wigner function. [Copyright &y& Elsevier]

Abstract: We consider generalizations of the Berry and Balazs nonspreading and accelerating solution of the time-dependent Schrödinger equation in empty space, which has been experimentally demonstrated in paraxial optics. In particular, we show that the original nonspreading wave packet is unstable. An explicit variation of the initial Airy-state evolves into the self-accelerating and self-compressing solution presented here. Quasi-diffraction-free finite energy Airy beams that are more realistic for experimental study are obtained by analytic continuation and their Wigner function is evaluated. Nonlinear generalizations related to second Painlevé transcendents are briefly discussed. [Copyright &y& Elsevier]

Abstract: Large-scale data are analysed using the Wigner function. It is shown that the ‘frequency variable’ provides important information, which is lost with other techniques. The method is applied to ‘sentiment analysis’ in data from social networks and also to financial data. [Copyright &y& Elsevier]

Abstract: Problem of unambiguous state discrimination of two squeezed states of light beam has been investigated. Wigner function of the two squeezed states is used to calculate their scalar product in order to determine optimal success probability of unambiguous discrimination. We propose a general scheme for unambiguous state discrimination using probabilistic quantum cloning for any two known pure quantum states. [Copyright &y& Elsevier]

Abstract: We describe both quantum particles and classical particles in terms of a classical statistical ensemble, with a probability distribution in phase space. By use of a wave function in phase space both can be treated in the same quantum formalism. Quantum particles are characterized by a specific choice of observables and time evolution of the probability density. Then interference and tunneling are found within classical statistics. Zwitters are (effective) one-particle states for which the time evolution interpolates between quantum and classical particles. Experimental bounds on a small parameter can test quantum mechanics. [Copyright &y& Elsevier]

Abstract: In this paper, the photon-added-then-subtracted squeezed vacuum state (PASSVS), a non-Gaussian state, is presented by adding then subtracting photon to a squeezed vacuum state. It is found that PASSVS is just a superposition state between S(r)|0〉 and S(r)|2〉, where S(r) is the single-mode squeezing operator with the squeezing parameter r. Its non-Gaussianity is exhibited via its Wigner function and the Hilbert–Schmidt distance. In addition, a possible scheme is presented to produce the PASSVS by virtue of the cavity QED. [Copyright &y& Elsevier]

Abstract: As a generalization of the optical circular states, elliptical states which are quantum superposition of coherent states on an ellipse in the α plane are constructed. The statistical properties of the states are investigated by using sub-Poissonian photon statistics, quadrature squeezing, Wigner function and phase distribution. It is shown that the elliptical states exhibit stronger quadrature squeezing. The interference fringes between the coherent states form the elliptic annuli of Fock states in the Wigner function picture. The phase distribution is no longer uniform as the circular states. An experimental scheme is proposed for generating equidistant coherent-state superpositions on an ellipse for the motion of the center of mass of a trapped ion. [ABSTRACT FROM AUTHOR]

Abstract: The propagation of nonparaxial, partially coherent fields may be modeled in many ways. The standard techniques of Huygens-type propagation integrals or plane-wave decompositions require quadruple oscillatory integrals that carry a significant computational cost. Two alternative, computationally efficient methods for such modeling are presented here. One uses a discrete nonparaxial basis expansion of the field, while the other uses Wigner functions for nonparaxial fields. Two possible nonparaxial generalizations of Gaussian Schell-model beams are presented and used to demonstrate the utility of the methods by computing the spatial distribution of several recently proposed definitions of the degree of polarization of a nonparaxial field. [ABSTRACT FROM AUTHOR]

Abstract: An appropriately prepared real-valued wave packet moving in one space dimension will focus during a brief period of time even in the absence of any force. We illustrate this phenomenon by considering the time evolution of the elementary superposition of the ground state and the second excited state of a harmonic oscillator. Moreover, we show that a variation of the superposition parameter leads us from a domain of enhanced spreading via a point of suppressed spreading to a region where the wave packets focuses before it spreads again. We determine the points of maximal spreading and optimal focusing. Our analysis of this unusual behavior of a free quantum particle rests on the time dependence of (i) the average separation of the wave packet from the origin, (ii) the probability density in position space, and (iii) the Wigner phase space distribution. We conclude our search for optimally focusing wave packets by solving the corresponding variational problem with respect to a family of measures expressing the width of the wave packet. [ABSTRACT FROM AUTHOR]