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Based on the Pauli spin operators we develop the notion of the spin-correlation matrix for the two-qubit system. If this matrix is non-zero, the measure of the correlation between the qubits is the average of the non-zero elements. Trivially, for zero matrix the bipartite is uncorrelated. This criterion turns out to be a necessary and sufficient condition for the full correlation, where it includes information on both entanglement and correlation other than entanglement. Moreover, we discuss to what extent this criterion can give information on the entanglement of the system. The criterion is generic in the sense that it can be applied to mixed and pure systems. Also, it can be easily extended to treat the correlation of multipartite systems. We compare the results obtained from this criterion to those from concurrence for various examples and we gain agreement regarding entanglement. We believe that this criterion may have a wide range of potential applications in quantum information theory., Comment: 15 pages, 4 figures. arXiv admin note: text overlap with arXiv:1106.3392

In this doctoral thesis we have studied the quantum properties of several models which have been classified as statical and dynamical systems. The first part has been devoted to investigate the properties of the statical models including the superposition of squeezed displaced number states with and without thermal noise. Also we have developed a new type of multidimensional squeeze operator including two different squeezing mechanisms. In the second part the dynamical models were given to show the interaction between modes in the nonlinear optical coupler., Comment: 151 pages, 36 figures; PhD Thesis. Department of Optics, Faculty of Natural Sciences, Palacky University, Olomouc, Czech Republic, July (2001). PhD Advisor: Prof. RNDr. Jan Perina, DrSc

In this communication we investigate the quantum statistics of three harmonic oscillators mutually interacting with each other considering the modes are initially in Fock states. After solving the equations of motion, the squeezing phenomenon, sub-Poissonian statistics and quasiprobability functions are discussed. We demonstrate that the interaction is able to produce squeezing of different types. We show also that certain types of Fock states can evolve in this interaction into thermal state and squeezed thermal state governed by the interaction parameters., Comment: 25 pages, 7 figures

The evolution of the Schr\"{o}dinger-cat states in a dissipative parametric amplifier is examined. The main tool in the analysis is the normally ordered characteristic function. Squeezing, photon-number distribution and reduced factorial moments are discussed for the single- and compound-mode cases. Also the single-mode Wigner function is demonstrated. In addition to the decoherence resulting from the interaction with the environment (damped case) there are two sources which can cause such decoherence in the system even if it is completely isolated: these are the decay of the pump and the relative phases of the initial cat states. Furthermore, for the damped case there are two regimes, which are underdamped and overdamped. In the first (second) regime the signal mode or the idler mode "collapses" to a statistical mixture (thermal field)., Comment: 34 pages, 10 figures

In this paper we derive the quantum statistical and dynamical properties of nonlinear optical couplers composed of two nonlinear waveguides operating by the second subharmonic generation, which are coupled linearly through evanescent waves and nonlinearly through nondegenerate optical parametric interaction. Main attention is paid to generation and transmission of nonclassical light, based on a discussion of squeezing phenomenon, normalized second-order correlation function, and quasiprobability distribution functions. Initially coherent, number and thermal states of optical beams are considered. In particular, results are discussed in dependence on the strength of the nonlinear coupling relatively to the linear coupling. We show that if the Fock state $|1>$ enters the first waveguide and the vacuum state $|0>$ enters the second waveguide, the coupler can serve as a generator of squeezed vacuum state governed by the coupler parameters. Further, if thermal fields enter initially the waveguides the coupler plays similar role as a microwave Josephson-junction parametric amplifier to generate squeezed thermal light., Comment: 32 pages, 10 figures

In this communication we discuss SU(1,1)- and SU(2)-squeezing of an interacting system of radiation modes in a quadratic medium in the framework of Lie algebra. We show that regardless of which state being initially considered, squeezing can be periodically generated., Comment: 13 pages, 3 figures

We show that a nonlinear asymmetric directional coupler composed of a linear waveguide and a nonlinear waveguide operating by nondegenerate parametric amplification is an effective source of single-mode squeezed light. This is has been demonstrated, under certain conditions and for specific modes, for incident coherent beams in terms of the quasiprobability functions, photon-number distribution and phase distribution., Comment: 17 pages, 4 figures

We show that a nonlinear asymmetric directional coupler composed of a linear waveguide and a nonlinear waveguide operating by nondegenerate parametric amplification is an effective source of single-mode squeezed light. This is has been demonstrated, under certain conditions and for specific modes, for incident coherent beams in terms of the quasiprobability functions, photon-number distribution and phase distribution., Comment: 19 pages, 5 figures

In [J.S. Shaari, M. Lucamarini, M.R.B. Wahiddin, Phys. Lett. A 358 (2006) 85-90] the deterministic six states protocol (6DP) for quantum communication has been developed. This protocol is based on three mutually unbiased bases and four encoding operators. Information is transmitted between the users via two qubits from different bases. Three attacks have been studied; namely intercept-resend attack (IRA), double-CNOT attack (2CNOTA) and quantum man-in-the-middle attack. In this Letter, we show that the IRA and 2CNOTA are not properly addressed. For instance, we show that the probability of detecting Eve in the control mode of the IRA is 70% instead of 50% in the previous study. Moreover, in the 2CNOTA, Eve can only obtain 50% of the data not all of it as argued earlier., Comment: 7 pages, 2 figures

In this Letter we describe a new two-mode system, which consists of Kerr-like medium and down conversion process, called the Kerr-down conversion system. Under a certain condition we can obtain an exact solution of the dynamical equations of motion. For this system we investigate different kinds of quadrature squeezing, e.g., single-mode, two-mode and sum-squeezing. Also we give a more general definition of the principal squeezing. We show that the amounts of nonclassical effects produced by the Kerr-like and down-conversion processes separately are greater than those obtained from the Kerr-down conversion system where both the processes are in competition., Comment: 12 pages, 3 figures

We make a comparative study of quadrature squeezing, photon-number distribution and Wigner function in a decayed quantum system. Specifically, for a field mode prepared initially in cat states interacting with a zero-temperature environment, we show that the rate of reduction of the nonclassical effects in this system is proportional to the occurrence of the decoherence process., Comment: 11 pages, 4 figures

In this paper, we study the quantum properties for a system that consists of a central atom interacting with surrounding spins through the Heisenberg $XX$ couplings of equal strength. Employing the Heisenberg equations of motion we manage to derive an exact solution for the dynamical operators. We consider that the central atom and its surroundings are initially prepared in the excited state and in the coherent spin state, respectively. For this system, we investigate the evolution of variance squeezing and entanglement. The nonclassical effects have been remarked in the behavior of all components of the system. The atomic variance can exhibit revival-collapse phenomenon based on the value of the detuning parameter., Comment: 19 pages,8 figures

Based on the Pauli spin operators we develop the notion of the spin-correlation matrix for the two-qubit system. If this matrix is non-zero, the measure of the correlation between the qubits is the average of the non-zero elements. Trivially, for zero matrix the bipartite is uncorrelated. This criterion turns out to be a necessary and sufficient condition for the full correlation, where it includes information on both entanglement and correlation other than entanglement. Moreover, we discuss to what extent this criterion can give information on the entanglement of the system. The criterion is generic in the sense that it can be applied to mixed and pure systems. Also, it can be easily extended to treat the correlation of multipartite systems. We compare the results obtained from this criterion to those from concurrence for various examples and we gain agreement regarding entanglement. We believe that this criterion may have a wide range of potential applications in quantum information theory., Comment: A new version placed as arxiv:1204.0341

The mixed states are important in quantum optics since they frequently appear in the decoherence problems. When one of the components of the system is prepared in the mixed state and the evolution operator of this system is not available, one cannot deduce the density matrix. We present analytical approach to accurately solve this problem. The approach can be applied on the condition that the Schr\"odinger's equation of the system is solvable with any arbitrary initial state. In deriving the solution we exploit the fact that any mixed state can be expressed in terms of a phase state. The approach is illustrated by deriving the density matrix of a single-mode heat environment interacting asymmetrically with two qubits. Our results are in good agreement with the available results in the literature. This approach opens new perspectives for treating complicated systems and may impact other applications in the quantum theory., Comment: 10 pages, 2 figures, comments are very welcome

In this paper, we study the quantum properties of the three-mode squeezed operator. This operator is constructed from the optical parametric oscillator based on the three concurrent $\chi^{(2)}$ nonlinearities. We give a complete treatment for this operator including the symmetric and asymmetric nonlinearities cases. The action of the operator on the number and coherent states are studied in the framework of squeezing, second-order correlation function, Cauchy-Schwartz inequality and single-mode quasiprobability function. The nonclassical effects are remarkable in all these quantities. We show that the nonclassical effects generated by the asymmetric case--for certain values of the system parameters--are greater than those of the symmetric one. This reflects the important role for the asymmetry in the system. Moreover, the system can generate different types of the Schr\"odinger-cat states., Comment: 21 pages, 14 figures; comments are most welcome

In this paper, we develop the notion of the linear atomic quantum coupler. This device consists of two modes propagating into two waveguides, each of them includes a localized and/or a trapped atom. These waveguides are placed close enough to allow exchanging energy between them via evanescent waves. Each mode interacts with the atom in the same waveguide in the standard way, i.e. as the Jaynes-Cummings model (JCM), and with the atom-mode in the second waveguide via evanescent wave. We present the Hamiltonian for the system and deduce the exact form for the wavefunction. We investigate the atomic inversions and the second-order correlation function. In contrast to the conventional linear coupler, the atomic quantum coupler is able to generate nonclassical effects. The atomic inversions can exhibit long revival-collapse phenomenon as well as subsidiary revivals based on the competition among the switching mechanisms in the system. Finally, under certain conditions, the system can yield the results of the two-mode JCM., Comment: 14 pages, 3 figures; comments are most welcome

The parametric amplifier with and without the pumping fluctuations of coupling function is considered when the fields are initially prepared in coherent light. The pumping fluctuations are assumed to be normally distributed with time-dependent variance. The effects of antibunching and anticorrelation of photons on the photon distribution, correlation between modes and factorial moments are demonstrated. A possible enhancement of photon antibunching for certain values of initial mean photon numbers is shown and discussed. We have shown also that new states (called modified squeezed vacuum states or even thermal states) can be generated from such an interaction. Further, we have demonstrated that the sum photon-number distribution can exhibit collapses and revivals in the photon-number domain somewhat similar to those known in the Jaynes-Cummings model., Comment: 17 pages, 6figures

For multiphoton intensity-dependent Jaynes-Cummings model (JCM), which is described by two-level atom interacting with a radiation field, we prove that there is a relationship between the atomic inversion and the quadrature squeezing. We give the required condition to obtain best information from this relation. Also we show that this relation is only sensitive to large values of the detuning parameter. Furthermore, we discuss briefly such relation for the off-resonance standard JCM., Comment: 14 pages, 6 figures

We investigate the squeezed regions in the phase plane for non-dissipative dynamical systems controlled by SU(1,1) Lie algebra. We analyze such study for the two SU(1,1) generalized coherent states, namely, the Perelomov coherent state (PCS) and the Barut-Girardello Coherent state (BGCS)., Comment: 18 pages, 9 figures

In this paper we discuss the quantum properties for superposition of squeezed displaced number states against multiphoton Jaynes-Cummings model (JCM). In particular, we investigate atomic inversion, photon-number distribution, purity, quadrature squeezing, Mandel $Q$ parameter and Wigner function. We show that the quadrature squeezing for three-photon absorption case can exhibit revivals and collapses typical to those occurring in the atomic inversion for one-photon absorption case. Also we prove that for odd number absorption parameter there is a connection between the evolution of the atomic inversion and the evolution of the Wigner function at the origin in phase space. Furthermore, we show that the nonclassical states whose the Wigner functions values at the origins are negative will be always nonclassical when they are evolving through the JCM with even absorption parameter. Also we demonstrate that various types of cat states can be generated via this system., Comment: 27 pages, 10 figures

In this paper we consider a system consisting of a two-level atom in an excited state interacting with two modes of a radiation field prepared initially in $l$-photon coherent states. This system is described by two-mode multiphoton (, i.e., $k_1, k_2$) Jaynes-Cummings model (JCM). For this system we investigate the occurrence of the revival-collapse phenomenon (RCP) in the evolution of the single-mode, two-mode, sum and difference quadrature squeezing. We show that there is a class of states for which all these types of squeezing exhibit RCP similar to that involved in the corresponding atomic inversion. Also we show numerically that the single-mode squeezing of the first mode for $(k_1,k_2)=(3,1)$ provides RCP similar to that of the atomic inversion of the case $(k_1,k_2)=(1,1)$, however, sum and difference squeezing give partial information on that case. Moreover, we show that single-mode, two-mode and sum squeezing for the case $(k_1,k_2)=(2,2)$ provide information on the atomic inversion of the single-mode two-photon JCM. We derive the rescaled squeezing factors giving accurate information on the atomic inversion for all cases. The consequences of these results are that the homodyne and heterodyne detectors can be used to detect the RCP for the two-mode JCM., Comment: 18 pages, 6 figures

In this paper we investigate the quantum phase properties for the coherent superposition states (Schr\"odinger-cat states) for two-mode multiphoton Jaynes-Cummings model in the framework of the Pegg-Barnett formalism. We also demonstrate the behavior of the Wigner ($W$) function at the phase space origin. We obtain many interesting results such as there is a clear relationship between the revival-collapse phenomenon occurring in the atomic inversion (as well as in the evolution of the $W$ function) and the behavior of the phase distribution of both the single-mode and two-mode cases. Furthermore, we find that the phase variances of the single-mode case can exhibit revival-collapse phenomenon about the long-time behavior. We show that such behavior occurs for interaction time several times smaller than that of the single-mode Jaynes-Cummings model., Comment: 23, 8 figures

In this paper we consider a system consisting of a two-level atom, initially prepared in a coherent superposition of upper and lower levels, interacting with a radiation field prepared in generalized quantum states in the framework of multiphoton Jaynes-Cummings model. For this system we show that there is a class of states for which the fluctuation factors can exhibit revival-collapse phenomenon (RCP) similar to that exhibited in the corresponding atomic inversion. This is shown not only for normal fluctuations but also for amplitude-squared fluctuations. Furthermore, apart from this class of states we generally demonstrate that the fluctuation factors associated with three-photon transition can provide RCP similar to that occurring in the atomic inversion of the one-photon transition. These are novel results and their consequence is that RCP occurred in the atomic inversion can be measured via a homodyne detector. Furthermore, we discuss the influence of the atomic relative phases on such phenomenon., Comment: 17 pages, 4 figures

In this paper, we investigate the single mode quantum properties of the codirectional Kerr nonlinear coupler when the frequency mismatch is involved and a condition for an exact solution of equations of motion is fulfilled. Particularly, we investigate quadrature and principal squeezing, Wigner function, quadrature distribution, phase distribution and phase variance. We show that the quadrature squeezing and the phase variance can exhibit collapse-revival and collapse-revival-subrevival phenomena, respectively, based on the values of the detuning parameter. Furthermore, we analytically demonstrate that the system can generate cat states, in particular, Yurke-Stoler states., Comment: 26 pages, 7 figures

We investigate the quantum properties for the codirectional three-mode Kerr nonlinear coupler. We investigate single-, two- and three-mode quadrature squeezing, Wigner function and purity. We prove that this device can provide richer nonclassical effects than those produced by the conventional coupler, i.e. the two-mode Kerr coupler. We show that it can provide squeezing and the quadrature squeezing exhibiting leaf-revival-collapse phenomenon in dependence on the values of the interaction parameters. In contrast to the conventional Kerr coupler two different forms of cat states can be simultaneously generated in the waveguides. We deduce conditions required for the complete disentanglement between the components of the system., Comment: 23 pages, 6 figures

In this Letter we study the evolution of the higher-order squeezing, namely, $n$th-order single-mode squeezing, sum- and difference-squeezing for the codirectional Kerr nonlinear coupler. We show that the amount of squeezing decreases when $n$, i.e. the squeezing order, increases. For specific values of the interaction parameters squeezing factors exhibit a series of revival-collapse phenomena, which become more pronounced when the value of $n$ increases. Sum-squeezing can provide amounts of squeezing greater than those produced by the $n$th higher-order ($n\geq 2$) squeezing for the same values of interaction parameters and can map onto amplitude-squared squeezing. Further, we prove that the difference-squeezing is not relevant measure for obtaining information about squeezing from this device., Comment: 13 pages, 3 figures

In this paper, we develop a quantum key distribution protocol based on the Greenberger-Horne-Zeilinger states (GHZs). The particles are exchanged among the users in blocks through two steps. In this protocol, for three-particle GHZs three keys can be simultaneously generated. The advantage of this is that the users can select the most suitable key for communication. The protocol can be generalized to $N$ users to provide $N$ keys. The protocol has two levels for checking the eavesdroppers. Moreover, we discuss the security of the protocol against different attacks., Comment: 10 Page, no figures. Comments are most welcome

In this paper, we study some quantum properties of a superposition of displaced squeezed two-mode vacuum and single-photon states, such as the second-order correlation function, the Cauchy-Schwartz inequality, quadrature squeezing, quasiprobability distribution functions and purity. This type of states includes two mechanisms, namely, interference in phase space and entanglement. We show that these states can exhibit sub-Piossonian statistics, squeezing and deviate from the classical Cauchy-Schwartz inequality. Moreover, the amount of entanglement in the system can be increased by increasing the squeezing mechanism. In the framework of the quasiprobability distribution functions we show that the single-mode state can tend to thermal state based on the correlation mechanism. Generation scheme for such states is given., Comment: 25pages, 7 figures

In this paper, we develop the notion of the marginal and density atomic Wehrl entropies for two-level atom interacting with the single mode field, i.e. Jaynes-Cummings model. For this system we show that there are relationships between these quantities and both of the information entropies and the von Neumann entropy., Comment: 13 pages, 3 figures, this is the final version

In this paper we consider multimode multiphoton Jaynes-Cummings model, which consists of a two-level atom, initially prepared in an excited atomic state, interacting with $N$ modes of electromagnetic field prepared in general pure quantum states. For this system we show that under certain conditions the evolution of the Wigner function at the phase space origin provides direct information on the corresponding atomic inversion. This relation is also valid even if the system includes Kerr-like nonlinearity, Stark shift effect, different types of the initial atomic state as well as moving atom. Furthermore, based on this fact we discuss for the single-mode case the possibility of detecting the atomic inversion by means of techniques similar to those used for Wigner function., Comment: 19 pages, 4 figures

The linear entropy, the von Neumann entropy and the atomic Wehrl entropy are frequently used to quantify entanglement in the quantum systems. These relations provide typical information on the entanglement in the Jaynes-Cummings model (JCM). In this Letter, we explain the origin of this analytically and derive a closed form for the atomic Wehrl entropy. Moreover, we show that it is more convenient to use the Bloch sphere radius for quantifying entanglement in the JCM instead of these entropic relations., Comment: 10 pages, 1 figure, comments are most welcome

In this paper we study the interaction between two-level atom and quantized single-mode field, namely, Jaynes-Cummings model (JCM). The field and the atom are initially prepared in the binomial state and the excited atomic state, respectively. For this system we prove that the revival-collapse phenomenon exhibited in the atomic inversion of the standard JCM can be numerically (naturally) manifested in the evolution of the squeezing factor of the three-photon (standard) JCM provided that the initial photon-number distribution of the radiation has a smooth envelope., Comment: 14 pages, 4 figures, Comments are most welcome

In this paper we consider a system of two two-level atoms interacting with a single-mode quantized electromagnetic field in a lossless resonant cavity via $l$-photon-transition mechanism. The field and the atoms are initially prepared in the coherent state and the excited atomic states, respectively. For this system we investigate the entropy squeezing, the atomic variances, the von Neumann entropy and the atomic inversions for the single-atom case. We show that the more the number of the parties in the system the less the amounts of the nonclassical effects exhibited in the entropy squeezing. The entropy squeezing can give information on the corresponding von Neumann entropy. Also the nonclassical effects obtained form the asymmetric atoms are greater than those obtained form the symmetric atoms. Finally, the entropy squeezing gives better information than the atomic variances only for the asymmetric atoms., Comment: 15 pages, 4 figures, comments are most welcome

In this paper, we study the interaction between the two-level atom and a bimodal cavity field, namely, two-mode Jaynes-Cummings model when the atom and the modes are initially in the atomic superposition state and two-mode squeezed vacuum state, respectively. For this system we investigate the atomic inversion, linear entropy and atomic Wehrl entropy. We show that there is a connection between all these quantities. Also we prove that the atomic Wehrl entropy exhibits behaviors similar to those of the linear entropy and the von Neumann entropy. Moreover, we show that the bipartite exhibits periodical disentanglement and derive the explicit forms of the states of the atom and the modes at these values of the interaction times., Comment: 12 pages, 4 figures

In this paper we study the evolution of the two two-level atoms interacting with a single-mode quantized radiation field, namely, two-atom multiphoton Jaynes-Cummings model when the radiation field and atoms are initially prepared in the superpostion of displaced number states and excited atomic states, respectively. For this system we investigate the atomic inversion, Wigner function, phase distribution and entanglement., Comment: 18 pages, 17 figures