acta physica slovaca, vol. 48, June 1998, no. 3

Special Issue on Quantum Optics and Quantum Information

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$\fbox{\epsfig{file=psfile.ps}}$ CONTENTS

$\fbox{\epsfig{file=psfile.ps}}$ Foreword

$\fbox{\epsfig{file=psfile.ps}}$ Asymmetric quantum cloning machines

Authors: N.J. Cerf
Abstract: A family of asymmetric cloning machines for quantum bits and N-dimensional quantum states is introduced. These machines produce two approximate copies of a single quantum state that emerge from two distinct channels. In particular, an asymmetric Pauli cloning machine is defined that makes two imperfect copies of a quantum bit, while the overall input-to-output operation for each copy is a Pauli channel. A no-cloning inequality is derived, characterizing the impossibility of copying imposed by quantum mechanics. If p and p' are the probabilities of the depolarizing channels associated with the two outputs, the domain in $(\sqrt{p},\sqrt{p'})$ -space located inside a particular ellipse representing close-to-perfect cloning is forbidden. This ellipse tends to a circle when copying an N-dimensional state with $N\to\infty$ , which has a simple semi-classical interpretation. The symmetric Pauli cloning machines are then used to provide an upper bound on the quantum capacity of the Pauli channel of probabilities p_x, p_y and p_z. The capacity is proven to be vanishing if $(\sqrt{p_x},\sqrt{p_y},\sqrt{p_z})$ lies outside an ellipsoid whose pole coincides with the depolarizing channel that underlies the universal cloning machine. Finally, the tradeoff between the quality of the two copies is shown to result from a complementarity akin to Heisenberg uncertainty principle. [page 115]

$\fbox{\epsfig{file=psfile.ps}}$ Optimal compression of quantum information for one-qubit source at incomplete data: a new aspect of Jaynes principle

Authors: M. Horodecki, R. Horodecki, P. Horodecki
Abstract: We consider the problem of optimal processing of quantum information at incomplete experimental data characterizing quantum source. In particular, we then prove that for one-qubit quantum source the Jaynes principle offers a simple scheme for optimal compression of quantum information. According to the scheme one should process as if the density matrix of the source were actually equal to the matrix of the Jaynes state. [page 133]

$\fbox{\epsfig{file=psfile.ps}}$ Entanglement and thermodynamical analogies

Authors: P. Horodecki, R. Horodecki, M. Horodecki
Abstract: We provide some new properties of entanglement of formation. In particular, we obtain an additive lower bound for entanglement of formation. Subsequently we develop the concept of local orthogonality of ensembles which leads to the mixed states with distillable entanglement equal to entanglement of formation. Then we consider thermodynamical analogies within the entanglement processing domain. Especially, we exploit analogy entanglement - energy. In this scheme the total entanglement i.e. the amount of singlet pairs needed for local preparation of a state corresponds to internal energy while the free entanglement defined as the number of pairs which can be recovered from the state (distillable entanglement) is the counterpart of free energy. In particular, it leads us to the question about ``temperature'' of entanglement. We also propose a scheme of the search of representative state for given entanglement which can be viewed as an analogue of the Jaynes maximum entropy principle. [page 141]

$\fbox{\epsfig{file=psfile.ps}}$ Remarks on search algorithms and nonlinearity

Authors: M. Czachor
Abstract: Nonlinear data search algorithms proposed recently by Abrams and Lloyd [3] are fast but make an explicit use of an arbitrarily fast unphysical transfer of information within a quantum computer. It is shown that the algorithms can be described also in a fully local formalism. [page 157]

$\fbox{\epsfig{file=psfile.ps}}$ Entanglement and pseudomixtures

Authors: M. Kuna
Abstract: In a recent paper Sanpera et al. [Los Alamos e-print archive quant-ph/9801024] have shown, that for the simplest binary composite systems any density matrix can be described in terms of only product vectors. The purpose of this note is to show that possibility of decomposing any state as pseudomixtures does not depend on dimension of the subsystems. [page 163]

$\fbox{\epsfig{file=psfile.ps}}$ Application of quantum key distribution for mutual identification - experimental realization

Authors: M. Dusek, O. Haderka, M. Hendrych
Abstract: A secure quantum identification system combining a classical identification procedure and quantum key distribution is proposed. Each identification sequence is always used just once and new sequences are ``refuelled'' from a shared secret key transferred over a quantum channel. The question of authentication of information sent over a public channel is discussed. An apparatus using two unbalanced Mach-Zehnder interferometers has been built, and quantum key distribution and ``quantum identification'' have been successfully tested through a single-mode optical fibre at 830 nm, employing low intensity coherent states (below 0.1 photons per pulse). [page 169]

$\fbox{\epsfig{file=psfile.ps}}$ Controling the flow of information in quantum cloner: Asymmetric cloning

Authors: V. Buzek, M. Hillery, M. Bendik
Abstract: We show that the distribution of information at the output of the quantum cloner can be efficiently controlled via preparation of the quantum cloner. We present a universal cloning network with the help of which asymmetric cloning can be performed. [page 177]

$\fbox{\epsfig{file=psfile.ps}}$ Reconstruction of photon distribution with positivity constraints

Authors: K. Banaszek
Abstract: An iterative algorithm for reconstructing the photon distribution from the random phase homodyne statistics is discussed. This method, derived from the maximum-likelihood approach, yields a positive definite estimate for the photon distribution with bounded statistical errors even if numerical compensation for the detector imperfection is applied. [page 185]

$\fbox{\epsfig{file=psfile.ps}}$ Optimized tomography of observables

Authors: G.M. D'Ariano, M.G.A. Paris
Abstract: Tomographic measurement of observables is revisited, and an adaptive optimization of the kernel functions suggested. The method is based on the existence of a class of null functions, which have zero tomographic average for any state of radiation. The general procedure is illustrated, and application to relevant observables analyzed in details for coherent, squeezed and "cat" states. [page 191]

$\fbox{\epsfig{file=psfile.ps}}$ Reconstruction of diagonal elements of density matrix using maximum likelihood estimation

Authors: Z. Hradil, R. Myska
Abstract: The data of the experiment of Schiller et al. [Phys. Rev. Lett. 77(1996) 2933] are alternatively evaluated using the maximum likelihood estimation. The given data are fitted better than by the standard deterministic approach. Nevertheless, the data are fitted equally well by a whole family of states. Standard deterministic predictions correspond approximately to the envelope of these maximum likelihood solutions. [page 199]

$\fbox{\epsfig{file=psfile.ps}}$ Generating and monitoring Schrödinger cats in conditional measurement on a beam splitter

Authors: M. Dakna, J. Clausen, L. Knöll, D.-G. Welsch
Abstract: Preparation of Schrödinger-cat-like states via conditional output measurement on a beam splitter is studied. In the scheme, a mode prepared in a squeezed vacuum is mixed with a mode prepared in a Fock state and photocounting is performed in one of the output channels of the beam splitter. In this way the mode in the other output channel is prepared in a Schrödinger-cat-like state that is either a photon-subtracted or a photon-added Jacobi polynomial squeezed vacuum state, depending upon the difference between the number of photons in the input Fock state and the number of photons in the output Fock state onto which it is projected. Two possible photocounting schemes are considered, and the problem of monitoring cats that are ``hidden'' in a statistical mixture of states is studied. [page 207]

$\fbox{\epsfig{file=psfile.ps}}$ Resonance fluorescence of a driven two-level atom in a cavity with injected squeezed vacuum: Effect of the cavity frequency detuning

Authors: Peng Zhou, S. Swain
Abstract: We derive, in the bad cavity limit, an effective master equation for the reduced density matrix operator of a strongly driven atom coupled to a frequency-tunable cavity and damped by a squeezed vacuum. We find that the intensity, the resonance fluorescence spectrum and the photon-photon correlation of such an atom, emitted from the cavity, are strongly dependent upon the cavity resonance frequency and squeezing parameters. The enhancement and suppression of the fluorescence intensity and spectral peaks, spectral-line narrowing, and antibunching in fluorescence can be achieved in a prescribed manner by tuning the cavity and laser frequency, and by adjusting the squeezed photon number and phase. [page 221]

$\fbox{\epsfig{file=psfile.ps}}$ Disentanglement-preserving states in micromaser

Authors: M. Hillery, J. Skvarcek
Abstract: We consider micromaser fields which after interaction with one atom produce disentangled atom-field states. We find a special solution for which interaction with the atom has the effect of flipping the sign of the electric field. We also consider the general case and derive conditions which the field must satisfy. An example of the general solution is presented in the case that there is a trapping state at n=6. [page 239]

$\fbox{\epsfig{file=psfile.ps}}$ Cavity-induced atom-atom correlation for two unidentical atoms

Authors: M.S. Kim, G. Yeoman, Min Gyu Kim
Abstract: The mutual coherence of pairs of two-level atoms is studied for the case of unidentical atoms in a lossy cavity. It is established that the cavity can induce a correlation or anticorrelation of the atomic dipoles depending on the nature of the atom-atom and atom-cavity detunings. The cavity-induced atom-atom correlation is clearly manifested in the spectra of the cavity field and of the fluorescence field. [page 247]

$\fbox{\epsfig{file=psfile.ps}}$ Quantum eraser and the decoherence time of a local measurement process

Authors: Y. Abranyos, M. Jakob, J. Bergou
Abstract: We propose an implementation of the quantum eraser, based on a recent experimental scheme by Eichmann et al. [Phys. Rev. Lett. 70 (1993) 2359] involving two four-level atoms. In our version a continuous broad band excitation (BBE) field drives the two trapped atoms and information about which atom scattered the light is stored in the internal degrees of freedom of the atoms. Entanglement of the two atoms after the detection of the photon is intimately connected to the availability of this ``which path'' information. We also show that the quantum eraser can be used to measure the decoherence time of a local measurement process. [page 255]

$\fbox{\epsfig{file=psfile.ps}}$ Quantum synthesis of 3D vibrational states of trapped ions

Authors: B. Hladký, G. Drobný, V. Buzek
Abstract: A universal algorithm for a deterministic preparation of arbitrary three-mode bosonic states is introduced. In particular, we consider preparation of entangled quantum states of a vibrational motion of an ion confined in a 3D trapping potential. The target states are established after a proper sequence of laser stimulated Raman transitions. Stability of the algorithm with respect to a technical noise is discussed and the distance (fidelity) of outputs with respect to target states is studied. [page 271]

$\fbox{\epsfig{file=psfile.ps}}$ Second-order collapses and revivals

Authors: M. Kozierowski
Abstract: Second-order collapses and revivals caused by the photon-number mechanism in the Jaynes-Cummings model with a nonlinear Kerr medium and those in the Dicke model related to the collective mechanism are reviewed. The revival period of the oscillations is dependent on whether the initial mean photon-number $\bar{n}$ is integer or non-integer in the first case, and strongly related to the parity of either n (the photon number) if $n\!<\! A$ or A (the number of atoms) if $A\!<\!n$ in the latter. [page 281]

$\fbox{\epsfig{file=psfile.ps}}$ Quasidistributions for frequency converter model

Authors: A. Miranowicz, H. Matsueda, M.R.B. Wahiddin, J. Bajer
Abstract: We generalize, for arbitrary initial fields, the Glauber-Mista theorem of classical-like evolution of the frequency converter. We show, by solving completely the Orlov-Vedenyapin diagonalization problem, that the initially nonclassical fields remain nonclassical during the evolution of the frequency converter. We give a general expression for the two-mode Husimi Q-function and examples of its marginal (single-mode) quasidistributions for initial coherent states, Fock states and two-state superposition of Fock states. We find their graphical representations. [page 293]

$\fbox{\epsfig{file=psfile.ps}}$ Analytical results for the probe absorption spectrum of a driven two-level atom in a squeezed vacuum with finite bandwidth

Authors: R. Tanas, T. El-Shahat
Abstract: Analytical formulas for the probe absorption spectrum of a driven two-level atom damped to a squeezed vacuum with finite bandwidth are derived. We use the master equation approach to describe the evolution of the strongly driven two-level atom coupled to the reservoir being a squeezed vacuum with finite bandwidth produced by a degenerate parametric oscillator (DPO). The master equation is derived under the Born and Markov approximation which require the squeezed vacuum bandwidth to be much larger than the atomic linewidth, but not necessarily larger than the Rabi frequency of the driving field. Our master equation takes into account the detuning of the laser field from the atomic resonance. Examples of the absorption spectra are plotted and compared to their equivalents for the broadband squeezing. [page 301]

$\fbox{\epsfig{file=psfile.ps}}$ Holstein-Primakoff SU(1,1) coherent state in micromaser under intensity-dependent Jaynes-Cummings interaction

Authors: G. Ariunbold, J. Perina
Abstract: It is found that the Holstein-Primakoff SU(1,1)coherent state of the cavity field can be generated in a lossless micromaser under the weak Jaynes-Cummings interaction with intensity-dependent coupling of large number of individually injected polarized atoms. [page 315]

$\fbox{\epsfig{file=psfile.ps}}$ Quantum carpets made simple

Authors: I. Marzoli, F. Saif, I. Bialynicki-Birula, O.M. Friesch, A.E. Kaplan, W.P. Schleich
Abstract: We show that the concept of degeneracy is the key idea for understanding the quantum carpet woven by a particle in the box. [page 323]

$\fbox{\epsfig{file=psfile.ps}}$ On the connection between the quantum phase space functions of the oscillator and the angular momentum

Authors: P. Földi, M.G. Benedict, A. Czirják
Abstract: Using Schwinger's model of angular momentum it is possible to introduce general angular momentum phase space distributions by using two independent harmonic oscillators. We establish the connection between general and fixed jphase space functions. This is a reduction based on a relationship between the corresponding coherent states. [page 335]

$\fbox{\epsfig{file=psfile.ps}}$ Phase squeezed states

Authors: A.V.Chizov, M.G.A. Paris
Abstract: Phase squeezed states of a single mode radiation field have been introduced as eigenstates of a linear combination of lowering and raising operators. The explicit expression in the Fock basis has been obtained and some relevant properties have been illustrated. [page 343]

$\fbox{\epsfig{file=psfile.ps}}$ Stationary states in saturated two-photon processes and generation of phase-averaged mixtures of even and odd quantum states

Authors: V.V. Dodonov, S.S. Mizrahi
Abstract: We consider a relaxation of a single mode of the quantized field in a presence of one- and two-photon absorption and emission processes. Exact stationary solutions of the master equation for the diagonal elements of the density matrix in the Fock basis are found in the case of completely saturated two-photon emission. If two-photon processes dominate over single-photon ones, the stationary state is a mixture of phase averaged even and odd coherent states. [page 349]

$\fbox{\epsfig{file=psfile.ps}}$ Raman and Brillouin couplers with phase mismatch

Authors: J. Fiurásek, J. Perina
Abstract: Statistical properties of optical fields in asymmetric nonlinear couplers composed of two waveguides are investigated within the framework of a generalized superposition of coherent fields and quantum noise. Raman or Brillouin processes (with classical pumping) are in operation in the first waveguide. Stokes or/and anti-Stokes modes are connected through the linear interaction with corresponding modes in the second waveguide. Various phase mismatches are assumed. An approach to analytical solution of Heisenberg equations of motion is described. Various regimes for different values of Stokes and anti-Stokes linear coupling constants are discussed. An influence of various phase mismatches on the generation of nonclassical states of light including sub-Poissonian statistics, negative reduced factorial moments and squeezing of quadrature variances is investigated. [page 361]

$\fbox{\epsfig{file=psfile.ps}}$ Periodic behaviour of displaced Kerr states

Authors: W. Leonski
Abstract: We discuss quantum properties of displaced Kerr states, in particular the periodic behaviour of the mean values of various quantum parameters describing our model. Thus, we introduce an operator evolution approach that justifies our conclusions concerning the periodic behaviour of the system. [page 371]

$\fbox{\epsfig{file=psfile.ps}}$ Validity of the cumulant method for a pulse nonlinear Kerr oscillator

Authors: K. Grygiel, W. Leonski, P. Szlachetka
Abstract: We study the dynamics of an anharmonic oscillator driven by a train of pulses. The cumulant expansion and quantum evolution operator approaches are presented and compared. [page 379]

$\fbox{\epsfig{file=psfile.ps}}$ Some remarks about the Glauber-Sudarshan quasiprobability

Authors: A. Wünsche
Abstract: It is shown how two representations of the Glauber-Sudarshan quasiprobability in the Fock-state basis which are different in the form are related to each other and to the Sudarshan representation by the relations between the two-dimensional and the central-symmetric one-dimensional delta function and their derivatives. The regularized representation of the Glauber-Sudarshan quasiprobability by Perina and Mista is reconsidered in new light and is represented by introduction of the Laguerre 2D-functions. A new representation of the Glauber-Sudarshan quasiprobability by Hermite polynomials with a differentiation operator in the argument acting onto a one-dimensional delta function is found. The connections to representations of more generally ordered quasiprobabilities are established. It is shown that the convolution of the Glauber-Sudarshan quasiprobabilities for Fock states does not lead to a new Glauber-Sudarshan quasiprobability for a "physical" state corresponding to positively definite density operators. The Appendices present the derivation of identities including generalized which are relevant for many calculations in quantum optics. [page 385]

$\fbox{\epsfig{file=psfile.ps}}$ Radiation phase of a dipole radiation

Authors: A. S. Shumovsky
Abstract: In the case of a dipole electromagnetic radiation, the operator of the "radiation phase" is defined. It is shown that this operator has a discrete spectrum with eigenvalues, lying in the segment $[0,2 \pi ]$ . Some properties of the radiation phase and polarization are discussed. [page 409]

$\fbox{\epsfig{file=psfile.ps}}$ Book review

Related links: [Acta PhysicaSlovaca] [Institute of Physics, Bratislava] [Quantum Optics Group, Bratislava]

Gabriel Drobny
1998-07-15