Quantum neural nets

M.V. Altaisky

Joint Institute for Nuclear Research

The models and algorithms of quantum information processing, also called quantum computing, having been attracting attention since the pioneering works of Schor and Grover, that have proved the quantum computer to be capable of solving exponentially complex tasks in a polynomial time, with the factorization algorithm and the random database search algorithm have been presented. The quantum computing assumes the parallel processing of the data sets, those are in quantum superposition, by one or more quantum processors. The idea of deterministic algorithm is not rejected in this approach, but classical algorithm is merely substituted by quantum one. On the other hand, it is known that in complicated problems of nonlinear forecasting, data classification etc, often unsolvable by algorithmic methods, the non-algorithmic methods, based on self-organization, often turn to be effective. It seems, that extremely high efficacy of information processing in biological systems is due to a kind of quantum parallelism present there. These are the reasons to present this paper, where we review some models of non-algorithmic quantum information processing based on neural net ideas.

 

New surprises of quantum wave motion in external fields

Chabanov V.M., Zakhariev B.N.

BLTP, JINR

We show that the mechanism of spectral gap formation while switching on periodic perturbation has a 'hidden resonance' nature.This notion gives us paradoxically the key for understanding of wave behavior. The inversion technique  also gives rise to zone spectral control algorithms. Unexpected spectrum `reversion' appears to be attainable via the combination of two remarkable phenomena: resonance tunneling and Anderson's wave localization. "paradoxical" coexistence of continuum of 'bound' waves and discrete set of unlimited motion states.

We have found that potentials V(x) divided at arbitrary point x' in right-left parts Vr(x<x')=0, Vl(x>x')=0  have remarkable unexpected symmetry. There are continuous sets of equalities for penetrabilities of quite unequal separated Vr ¹ Vl.   Generalization of these equalities to wide classes of transformed Vr ,\, Vl potentials and even arbitrary initial potentials V(x) are given. Such equalities serve us as instructive illustrations enriching our quantum intuition useful for quantum engineering, etc.

 

A C#  package for assembling quantum circuits and generating associated polynomial sets

Vladimir P.Gerdt and Vasily Severyanov

Laboratory of Information Technologies
Joint Institute for Nuclear Research
141980 Dubna, Russia
gerdt@jinr.ru     severyan@jinr.ru

In [1] it was shown that elements of the unitary matrix determined by a quantum circuit can be computed by counting the number of common roots in Z2 for a certain set of multivariate polynomials over Z2. Given a quantum circuit, the polynomial set is uniquely constructed. In this talk we present a C#  package called QP (Quantum Polynomials) that allows a user to assemble a quantum circuit and to generate the multivariate polynomial set associated with the circuit.

The generated polynomial system can further be converted into the canonical bases form for the lexicographical monomial order. Grobner bases form the most universal algorithmic tool of modern computer algebra to investigate and solve systems of polynomial equations [2]. Construction of the lexicographical basis substantially alleviates the problem of the root finding for polynomial systems. To construct such a basis one can use efficient involutive algorithms developed in [3]. Our QP package together with a basis software provides a tool for simulation of quantum circuits. We illustrate this tool by example from [1].

[1] Christopher M. Dawson et al. Quantum computing and polynomial equations over the finite field Z2. arXiv:quant-ph/0408129, 2004.

[2] B.Buchberger and F.Winkler (eds.) Bases and Applications. Cambridge University Press, 1998.

[3] Gerdt V.P. Involutive Algorithms for Computing Groebner Bases. Proceedings of the NATO Advanced Research Workshop "Computational commutative and non-commutative algebraic geometry" (Chishinau, June 6-11, 2004), IOS Press, 2005.

 

Conditional Probability and Einstein-Podolsky-Rosen Paradox

V.V. Belokurov, O.A. Khrustalev, O.D. Timofeevskaya

Quantum Theory and High Energy Physics div., Faculty of Physics, Moscow State University

It was exactly 70 years ago when  15-th May  1935 the famous article   by A.Einstein, B.Podolsky and N.Rosen  [Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?] was published in Physical Review. In our communication we recall the history of quantum mechanics and the questions that were posed in this article. The communication  discusses how quantum mechanics answers to these questions . The concepts of quantum mechanics such that quantum states, conditional probability, conditional density matrix, etc. are considered.

 

Weakly coupled quantum wires and layers as an element of quantum computer

Popov I.Yu., Gortinskaya L.V., Gavrilov M.I., Pestov A.A., Tesovskaya E.S.

St.-Petersburg State University of Information Technologies, Mechanics and Optics

Nanostructures of waveguide type with weak coupling are considered. Main terms of the asymptotic expansion (in the coupling constant) of quasi eigenvalue close to the threshold are obtained for two different cases: semiconductor structures and sandwich magnetic-nonmagnetic metallic structures. It corresponds to different boundary conditions for the wave function of the electron (the Dirichlet condition or combined Dirichlet-Neumann condition). Scattering problem is considered in the framework of the asymptotic approach, and resonance effects for  the electron transport are described. Possible applications to quantum computing are discussed. 

 

Monodromy approach to quantum computing

G. Giorgadze

Institute of Cybernetics of the Georgian Academy of Sciences

A geometric model of quantum computing is considered, where the encoded space of information is the fibre of holomorphic vector bundle with logarithmic connection on a manifold with nontrivial topology. This model is an analog of the holonomic quantum computing and uses the properties and specifics  of  logarithmic connections. The holonomy operator acts on the qubits as products of monodromy matrices, which makes it independent of the integration path.   We show, that in the case of irreducible  connection we obtain in this way all local gates.    

 

Control of the atom’s center-of-mass motion in a quantized trap, with the help of a classical light field.

G.P. Miroshnichenko

St.Petersburg State University of Information Technologies, Mechanics and Optics.

The model of Blockley, Walls, Risken, describing interaction of the atom’s center-of-mass motion with intra-atomic transition, was generalized. In accordance with model, this interaction arises, when the atom in a quantized (parabolic) trap set in the node of EM standing wave, tuned to one of the vibrational sidebands of the atomic transition. In the first generalization we suppose, that the additional traveling wave was tuned to resonance with atomic transition. In that case the vibrational mode will be exited into the coherent state with certain (average) numbers of photons and the atom will oscillate with definite amplitude in a potential of the trap. In the second generalization we switch on the two-mode, near resonance EM field. As is shown, the vibrational mode will be exited in the squeezing state on certain choice of the frequencies and two-mode field strength. The coordinate or the moment of the atom’s center-of-mass will have the property of squeezing with definite choice of phase of the two-mode field. The atom in the squeezing state is localized in the coordinate space or in the momentum space of a trap. It is showed, that the transition in the squeezing states take place under a slowly varying amplitude of EM field. The evaluation of a closing speed depending on parameters of a model was made.

 

Quantum Cellular Automata: Challenges and Possible Applications

Alexander Yu. Vlasov

Federal Radiology Center (IRH), 197101 Mira Street 8, St.–Petersburg, Russia

Quantum cellular automata (QCA) and quantum lattice gas automata (QLGA) may have different definitions, but there are particular cases [1, 2], which have clearer correspondence with classical analogues.

One challenge of QCA in comparison with classical case — is usual topic with treatment of subsystem in quantum mechanics. Even if whole QCA may be described by pure state, it is not necessary so for single cell or block of cells used for definition of local transition function. It is possible to use density matrices or Heisenberg picture [1] to partially avoid such problem, but it may hide some essential aspects. On the other hand, work with pure states [2] (traditional for some QC tasks) may make consideration quite complicated. Yet another challenge — is difficulty in using of considered classes of QCA as models of physical processes. It is usual application of classical CA, but already for reversible CA appear some subtleties and quantum case even more complicated [1, 2]. Here QLGA may be more adequate choice, and exists some intriguing relation between QLGA and QCA resembling application of Fock space in quantum theory [2].

On the other hand, there are promising perspectives of QCA/QLGA applications and the models attract more attention last time. There is also related themes suffering currently active development, like quantum walk and applications of quantum 1D structures (e.g., Heisenberg chain) for state transfer and other tasks.

It should be also mentioned utilization of QCA/QLGA for deterministic programmable quantum processors (DPQ-processors) [3, 4]. The specific property of DPQ-processors with alternated application of “shift” and “control” quantum gates [3] has direct correspondence with so-called reversible Margolus CA used as predecessor of a QCA design mentioned here [1, 2, 4]. DPQ-processors need for very intensive data feeding on pseudo-classical bus [3] and QCA/QLGA may be considered as a good opportunity for resolution of the problem.

[1] B. Schumacher and R.F. Werner, Preprint quant-ph/0405174 (2004).

[2] A.Yu. Vlasov, Preprint quant-ph/0406119 (2004). CA Demo http://qubit.csa.ru/vlasov

[3] A.Yu. Vlasov, Preprint quant-ph/0205074; Part. Nucl. Lett. 1 60 (2003).

[4] R. Raussendorf, Preprint quant-ph/0412048 (2004).

 

Entangled Solitons and Stochastic Qubits

Yu.P. Rybakov, T.F. Kamalov

Physics Department, Moscow State Open University

Two solitons configurations are used for constructing entangled states in generalized quantum mechanics dealing with extended particles, endowed with nontrivial spin S. Stochastic realization of the wave function permits one to use the random Hilbert space and construct stochastic qubits serving the base for quantum computing simulation.

 

Simulation of N-qubit quantum systems: A computer-algebraic approach

S. Fritzsche, T. Radtke and A. Surzhykov

Department of Physics, Kassel University

Despite of the promising advancements in the present understanding of quantum computations and quantum information, there are still a large number of difficulties to be solved. One of the great challenges, for instance, refer to the decoherence in quantum systems and to the coupling of these systems with their environment. -- To overcome these difficulties, several schemes for studying the decay of quantum states and for the creation of entanglement have been developed in the past decade, including a variety of measures, decoherence-free subspaces as well as (quantum) error correction codes.

To support the investigation of entanglement and decoherence phenomena in general N-qubit quantum systems, we recently developed the FEYNMAN program, a computer-algebraic approach within the framework of Maple, which facilitates the symbolic and numerical manipulation of quantum registers and quantum transformations. It has been designed moreover for studying the dynamics of  quantum registers owing to their interaction with external field and perturbations. In this contribution, the set-up and use of this program is explained. For atomic photoionization, in particular, it is shown how (quantum) information and entanglement transfer arises from the incoming photons to the emitted photoelectrons. Detailed calculations have been carried out and will be discussed on the entanglement as function of the energy and polarization of the incoming light, the nuclear charge of the ions as well as the emission angle of the photoelectrons.

 

Quantum Systems in Regular and Stochastic Fields. Creation and Destruction of the Coherence.

Alexander V. Gorokhov

Department of General and Theoretical Physics of Samara State University

The problem of the coherent states generation with definite parameters for multilevel quantum systems is investigated. The interaction with external environment and stochastic fields can destroy of the coherence. The competition of these processes is considered on a base of Fokker - Planck Equations approach, deriving from master equation for the density matrix of the system.

Examples of dynamics of coherent states for two-level atoms in an external electromagnetic field and the entangled states generation in model of dipole-dipole interacting two-level atoms in the nonideal resonator by the influence of a short resonant light pulse are considered.

 

Time-modulated entangled states of light

Kryuchkyan G.Yu. and Adamyan H.H.

Yerevan State University

We propose time-modulated entangled states of light beams for time-resolved quantum information technologies which are now in the stage of development. As proper devices, new schemes of nondegenerate optical parametric oscillator: (i) driven by continuously modulated pump field; (ii) under action of a periodical sequence of identical laser pulses are elaborated. The schemes considered in contrast to many other entangled light sources operate under non-stationary conditions. We have shown that this circumstance has a significant impact on formation of continuous-variable entanglement in the presence of dissipation and cavity induced feedback and leads to a high degree of quadrature entanglement obeying the condition of EPR-like paradox criterion. We stress that the properties of EPR entanglement can be widely controlled via the modulation parameters. Another point of our studies is that all squeezing results and protocols have done in the time domain and not in the frequency domain.

 

Cloning entanglement of a pair of d-dimensional quantum states

E. Karpov, P. Navez, N.J. Cerf

Quantum Information and Communication Ecole Polytechnique

University Libre de Bruxelles

We propose an optimal quantum cloning machine that duplicates the entanglement of any given d-dimensional bipartite quantum state. It maximizes the amount of entanglement contained in two copies of maximally entangled input states preserving the separability of input unentangled pairs.

We analyze the entanglement of the clones in terms of the entanglement of formation and show that by optimization of the cloning machine in terms of fidelity leads to the maximization of the entanglement of the clones. For large d, the entanglement of formation for each clone tends to one half of the entanglement of input state, being always below this level.

 

Taking into account the pixel structure of photodetecting in an optical information channel with dense coding

Yu. Golubev, T. Golubeva, I. Sokolov, M. Kolobov

V. A. Fock Physics Institute, St. Petersburg State University

The theoretical approach to take into account the pixel structure of photodetecting in the information channel on the base of the Mach Zehnder interferometer with use of the squeezed light from the parametrical sources is considered. 

 

The Shannon information for the dense coding protocol

T. Golubeva, Yu. Golubev, I. Sokolov, M. Kolobov

V. A. Fock Physics Institute, St. Petersburg State University

In the dense coding information scheme, constructed on the basis of the Mach-Zehnder interferometer, the protocol for images transfering is elaborated. The formula for the information capacity of the channel is given in the explicit analitical form. The numerical treatment is presented as the curves.

 

Superradiance and laser cooling in solids

Bashkirov E.K.

Samara State University

The collective dynamics of the impurities in solids interacting with electromagnetic fields and local phonons has been considered. The role of superradiance effect in the cooling processes has been investigated.

 

Quantum Effects at Two Coupled Nonlinear-Optical Processes

Andrey V. Rodionov and Anatoly S. Chirkin

M.V. Lomonosov Moscow State University, Department of Physics,

Chair of General Physics and  Wave Processes


The coupled nonlinear-optical processes under consideration include the process of nondegenerate parametric down-conversion which is followed by the simultaneous sum-frequency generation process. The so-called reordered form of the unitary evolution operator has been deduced in our previous works, and on the besis of those results expressions for the output field state have been calculated for the cases of special initial fields: fields in coherent state at one or several interacting frequencies or fields with given photon number. It has been shown that the multiphoton entangled states are generated at the crystal's output. Quantum statistical properties (mean photon numbers, variances, correlation functions) have been studied. Quantum Zeno-like dynamics has been revealed.

 

Simultaneous Parametric Amplification and Up-Conversion of Optical Image

E.V. Makeev and A.S. Chirkin

Faculty of Physics, M.V. Lomonosov Moscow State University

We consider parametric image amplification realized by means of two consecutive processes. Carrier frequency of image is lower than pump frequency. At first stage image amplification occurs at carrier frequency. Next stage is frequency up-conversion to high frequency. The processes can be implemented simultaneously in the same nonlinear periodically poled crystal at the quasi-phase-matching condition. Mean photon numbers and signal-to-noise ratios are calculated for image at high frequency. The expressions obtained take into account size of pixel and time of measurement.

 

The entanglement of two qubits in bad cavity

A.M. Basharov, A.A. Bashkeev.

Moscow Engineering State University

This work tackles the problem of generation of entanglement between two two-level atoms embedded in a bad cavity. The simplest case of a system considered by Gao-xiang Li, K. Allaart and D. Lenstra (Phys. Rev. A 69, 055802 (2004)) is investigated. A system with no dipole-dipole interaction and no interaction with single thermostats is considered. A common broadband thermostat is assumed to have a zero temperature, so no excitation can be transmitted from the thermostat to the cavity. We investigated quantum evolution of one and two excitation in this system. It was found, that time dynamics of entanglement depends also from initial excitation of the mode field, that was not reported in mentioned paper. Stationary entanglement doesn’t depend from the initial excitation of the resonator mode, but it depends from the initial excitations of atomic system. Such behavior is similar to the system directly interacting with common broadband thermostat.

A vivid peculiarity of entanglement in diatomic systems is demonstrated: one could examine stationary density matrix only in conference with its time evolution in order to prove that there exists such initial conditions that leads to the given values of stationary density matrix elements.

 

Entanglement of a quantum states of noninteracting particles.

A.M. Basharov, A.A. Bashkeev, E.A. Manykin

RRC Kurchatov Institute

Perturbation theory rows contain entangled states of noninteracting systems in any order. It is evident that such “entanglement” should be distinguished from real entanglement. Examples of such treatment are given in this work.

 

Quantum memory for light -- perspectives of spatially multimode generalization

Denis Vasiliev1, Ivan V. Sokolov1, and Eugene S. Polzik2

(1) V. A. Fock Physics Institute, St. Petersburg University,
ul. Ul'anovskaya 1, Stary Petershof, 195904 St. Petersburg, Russia

(2) Niels Bohr Institute, Danish Quantum Optics Center -QUANTOPT, Copenhagen University,
Blegdamsvej 17, 2100 Copenhagen O, Denmark

e-mail: sokolov@is2968.spb.edu

In the past decades such novel field of application of quantum states of light and matter have emerged, as quantum information. Here one of important problems is the problem of light-matter quantum interface and quantum memory for light, that is, of the scheme allowing for the effective exchange (transfer, storage and readout) of quantum state between light and long-lived matter degrees of freedom. Such interface will be an essential component of quantum computation and quantum communication protocols.

The model of quantum memory for light based on quantum entanglement between a spatially single mode light wave and an ensemble of spin oriented atoms was proposed and extensively studied, both in theory and in experiment with Cs vapour cells, by Polzik et al [1, 2]. Quantum entanglement is due, on the one hand, to the polarization sensitive non-demolition type interaction, associated with the light induced atomic level shifts, and, on the other hand, to the difference homodyne detection of the output light, which plays a role of the Bell measurement.

In this communication we describe the essentially multivariate (spatially multimode) parallel model for quantum memory for light, based on the multivariate quantum entanglement. We expect that such a scheme will greatly improve the information capacity of its single mode version. The physical base for parallel spatially multimode scheme provide (i) the single mode protocol and (ii) the quantum properties of spatially multimode light fields, extensively studied in the novel field of quantum imaging. Of particular relevance is the multimode parallel spatio-temporal teleportation protocol [3, 4], called by the authors quantum holographic teleportation, which allows for an effective teleportation of quantum state of the input light beam with high resolution in space and time.

[1] E.S. Polzik et al, in: S.L. Braunstain and Arun K. Pati (Editors). Quantum information with continuous variables. Kluwer, Dordrecht (2003).

[2] B. Julsgaard, J. Sherson, J. Fiurasek, J. I. Cirac, and E.S. Polzik, Nature (London), 432, 482 (2004).

[3] I.V. Sokolov, M.I. Kolobov, A. Gatti, L.A. Lugiato, Opt.Comm., 193, 175 (2001).

[4] A. Gatti, I.V. Sokolov, M.I. Kolobov, and L.A. Lugiato, Eur.Phys.J. D 30, 123 (2004).

 

Quantum holographic teleportation of optical images with frequency conversion

Liubov Magdenko1, 2, Mikhail I. Kolobov2, and Ivan V. Sokolov1

(1) V. A. Fock Physics Institute, St. Petersburg University,
ul. Ul'anovskaya 1, Stary Petershof, 195904 St. Petersburg, Russia

(2) Laboratoire PhLAM, Universite de Lille 1,
59655 Villeneuve d'Ascq Cedex, France

e-mail: sokolov@is2968.spb.edu

Continuous variable quantum teleportation of a single-transverse-mode electromagnetic field has been demonstrated experimentally [1]. Recently there was a theoretical proposal of {\sl quantum holographic teleportation} of optical images [2, 3], that generalizes the teleportation protocol [1] to spatially multimode electromagnetic fields. The teleportation protocol [2, 3] has been called holographic because one can consider it as an extension of conventional holography to quantum domain. The reconstructed image is a quantum copy of the original image with fidelity that can be made close to unity. To achieve high fidelity in holographic teleportation is impossible with classical light and one has to use multimode entangled states of light.

In this communication we describe a new version of holographic teleportation that allows for the colour (frequency) conversion between the input and the teleported images. An input image is teleported to an output image at different frequency with preservation of its original multimode quantum state.

One of the most challenging problems of quantum information is that of quantum interface between the objects of different physical nature [4]. For an efficient resonant interaction between the light and the atoms it is often desirable to have a tunable source of light that does not change its quantum state in the tuning process. Our frequency tunable teleportation scheme just provides this possibility.

We describe the optical scheme of the new holographic teleportation protocol. The source of the spatially multimode entanglement in our scheme is a type-I traveling-wave non-degenerate optical parametric amplifier (OPA). We evaluate the quantum fluctuations in the new teleportation scheme and estimate the spatio-temporal scales and quality of the effective quantum state transfer between the spatially multimode light waves of different colours.

[1] A. Furusawa et al, Science, 282, 706 (1998); W. P. Bowen et al, Phys. Rev. A 67, 032302 (2003).

[2] I. V. Sokolov, M. I. Kolobov, A. Gatti, L. A. Lugiato, Opt. Comm., 193, 175 (2001).

[3] A. Gatti, I. V. Sokolov, M. I. Kolobov, and L. A. Lugiato, Eur. Phys.J. D 30, 123 (2004).

[4] B. Julsgaard, J. Sherson, J. Fiurasek, J.I. Cirac, and E.S. Polzik, Nature (London), 432, 482 (2004).

 

Quantum decoherence in the theory of open quantum systems

Aurelian Isar

Department of Theoretical Physics,

National Institute of Physics and Nuclear Engineering,

Bucharest-Magurele, Romania

In the framework of the Lindblad theory for open quantum systems, based on quantum dynamical semigroups, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum decoherence which is more and more significant in time. We calculate also the decoherence time scale and analyze the transition from quantum to classical behaviour of the considered system.

 

Many-to-many teleportation of a d-level system and broadcasting of entanglement

Iulia Ghiu

University of Bucharest

Department of Physics

In the original one-to-one teleportation protocol of Bennett et al., an observer Alice transmits the information of a d-level system to another observer Bob with perfect fidelity, by using a maximally entangled state.

We introduce here a generalization called the many-to-many teleportation, where the information is sent from N observers to M receivers situated at different locations.

One of the most interesting application of quantum cloning is the symmetric broadcasting of entanglement proposed by Buzek et al. We propose broadcasting of entanglement based on local and nonlocal optimal universal asymmetric cloning machines. By applying the Peres-Horodecki criterion we analyze the inseparability of the final states and then compute their fidelities.

 

Macroscopic entangled states

V.N. Gorbachev, A.Ya. Kazakov, A.I. Trubilko.

Laboratory of Quantum Information & Computation,

State University of AeroSpace Instrumentation, St.-Petersburg

Interaction between ensemble of two-level identical atoms and three-mode light is considered, when one of the modes is classical and its Rabi frequency much exceeds the effective Rabi frequencies of the remainder quantized modes. An effective Hamiltonian, that describes a process like non-degenerated down conversion, is found and statistics of quantized modes is discussed with use of exact solution of the Schrodinger equation for field in the Fock-Bargmann representation. It is found that occupation number of each quantized mode can exponentially depend on the number of atoms and the light state may be squeezed. The obtained squeezing is nearly perfect and results in an continuous analog of the maximally entangled EPR state of the light with macroscopic large number of photons.

V.N. Gorbachev, A.Ya. Kazakov, A.I. Trubilko, Journ. Opt. B, 2004, v.6, 517-524.

 

Quantum optical device accelerating dynamic programming

D. Grigoriev (1), A. Kazakov (2),  S. Vakulenko (3)

(1) IRMAR Universit'e de Rennes, Beaulieu, 35042, Rennes, France

(2) Institute for Aerospace Instrumentation, St. Petersburg, Russia

(3) Institute of Mechanical Engineering Problems, S. Petersburg, Russia

In this paper  we discuss analogue computers based on quantum optical systems accelerating dynamic programming for some computational problems.  These computers, at least in principle, can be realized by actually existing devices.  We estimate  an acceleration in resolving of some NP-hard problems that can be obtained in such a way versus  deterministic computers.

 

On the measurement based quantum gates from biphotons

Yu. A. Asikritova, I.D. Balatsky, V.N. Gorbachev.

Nor'Westerly Institute of Printing of St.-Petersburg  State

University of Technology and Design

Quantum measurement, which can be used as primitive for computation, is a main resource of the one-way quantum computer introduced by Briegel. In this model any computation is performed by a set of the one-way gates and  the multiparticle entangled states, known as cluster or graph states are exploited. In our work a set of deterministic gates based the quantum measurement and teleportation is considered. These gates involve bipartite entanglement,  allow  performing any operations on qubits and can be implemented from biphotons.

 

Properties of the W - like states with hierarchic organization

Anastasia Rodichkina and Valery Gorbachev

North-West Institute of Printing of St.-Petersburg State University of Technology and Design

Large number of multimode entangled states of light generated in down conversion processes belongs to a collection which is natural generalization of the W class introduced by Cirac et al. In this work we introduce this collection, a W-like class, and consider it from point of view of quantum information theory without referring to any physical system. We calculate several measures of entanglement and found, that some members from W like class can be reduced to the Dicke and Zero Sum Amplitude states and have hierarchy organization. Hierarchy organization allows to accomplish directly all protocols based on two-particle entanglement and we found, for example, teleportation and dense coding schemes using the multiparticle channel of the W like class. By this way an unknown multiparticle entangled states can be teleported using only 2 bits of classical information. For the multiparticle dense coding we found that it needs measuring all qubits to gain information, when measurement is performed on a part of them, then always 1 bit can be accessible. This feature seems to be attractive for protection of receiving station.

 

Hollow core photonic crystal fiber dispersion characteristics

Irina A. Khromova, Leonid A. Melnikov

Saratov State University

This work presents an effective hollow core photonic crystal fiber dispersion characteristics computational technique and an algorithm of discrimination between surface and localized waves. 

Entanglement in the Schredinger experiment

Issaeva E.A.

Institute of Physics, National Academy of Sciences of Azerbaijan

It is known that superposition of states  taking place in the quantum world can occur in the macroworld  too due to the mechanism of intensification. “Schrodinger cat” is a fact of such intensification. It is known that in an open system the “Schrodinger cat” paradox  is explained by the decoherence  phenomenon  but in a close system it is explained  by the many-world interpretation of quantum mechanics Everett-Wheeler.  The quantum real world is presented as a certain complex multi-spatial geometric figure and  what we call the “classical” world is one of face of this figure. In the paper it has shown that the this complex figure constitutes  the simplex notion in the functional analysis.  It has been shown that such an interpretation of mechanics enables one to obtain the non-uniform wave equation and the Schrodinger equation is the uniform equation of this equation.

 

Quantum Measurements and Decoherence in QM Operators Algebras Formalism

S.N. Mayburov

Lebedev Inst. of Physics, Leninsky Prospect 53, Moscow, Russia,

RU-117924 E-mail: Mayburov@sci.lebedev.ru

It's shown that C* Algebras formalism of Algebraic QM provides the consistent description of the quantum measurements with the account of decoherence by an arbitrary complex environment E [1]. In this formalism any system characterized by its Segal Algebra of observables U which defines the set W of system states j via GNS duality [2]. As the example the binary information system O regarded which measures observable Q of bynary pure state S - the superposition of several Q eigenstates |si> via S-O interaction HS,O . The joint state of S, O system' j S,O is defined on S-O Algebra U , after S-O interaction it describes the entangled state of S-O system relative to some external observer O’. The effective information transfered from S to O responds to the change of O internal (restricted) state j O defined on the subalgebra UOÎ U which includes only O internal observables [3]. It's shown that in the regarded example UO consists of the single 'pointer' observable QO. From Segal Theorem [2] j O is the classical state and in the individual event n it becomes the stochastic state j O( n ) = x Oi which appears with the well-known QM probabilities Pi. Therefore j O describes the random information pattern qi acquired and memorized by O , which corresponds to S pure state collapse [2, 3].

Algebraic formalism accounts also O final state decoherence from the interaction with E, which can be both the closed and open system of arbitrary complexity . In this case for S measurement the system states j S,O,E are defined on S, O , E algebra U’; yet O final states j O are defined on the same subalgebra UO , hence that states are largely analogous to the regarded j O restricted states of S, O system.

[1] S.Mayburov, 'Doublet States Formalism in Quantum Measuremen ts' Proc. of V Quantum Communications, Measurements and Computations Conf.,Capri, 2000, (Kluwer, N-Y,2001), Quant-ph / 0404153

[2] G.Emch 'Algebraic Methods in Statistical Physics and Quantum Mechnics' (Wiley , N-Y, 1972)

[3] T.Breuer, 'Subjective Decoherence in Quantum Measurements' Synthese 107, 1 (1996); 2

 

Study of electorostatic potentials of DNA promotors

T.P. Akishina, V.V. Ivanov, R.V. Polozov, V.S. Sivozhelezov

LIT, JINR

The approach allowing to calculate electrostatic potentials of long nucleotide sequences of DNA was developed. It is based on multigrid method of solving Poisson-Boltzmann equation, in which the time of calculation is proportional to N. It allows to perform calculations for several hundreds of nucleotide bases pairs. We consider 411 pairs long intervals of E.Coli promotors.

The performed analysis shows that the distribution of electrostatic potential around genom can help in solving the problem of classification of different parts of DNA sequences. At the same time, joint data including primary and secondary structure and physical properties of different DNA parts forms a reliable basis for classification of DNA promotors. The obtained results are extremely important for directed influence on the process of transcription, which means that they have perspective in medical and biotechnological applications.

 

Statistical simulation of non-coherent noises in Hilbert space and pseudo-pure states characteristics

A.Yu. Bogdanov1, Yu.I. Bogdanov2, S.P. Kukik1

(1) Moscow M.V. Lomonosov State University, Russia

(2) Institute of Physics and Technology, Russian Academy of Sciences

We consider a statistical mechanism of pseudo-pure state generation. The states are constructed by ensemble rounding of non-coherent noise. The dependence of fidelity and pseudo-pure component weight in the mixture on the number of ensemble representatives in rounding for various Hilbert space dimensions and noise power is studied using the statistical modeling method.

The effect of absolute robustness of the first principal component in Fourier-state density matrix rounding is discovered.

The method of pure state extraction by the means of Fourier transform and auxiliary qubits implementing is proposed. The effect of decoherence suppression by Zeno effect is considered.

 

Phase-polarization meashurements in coherent microscopy.

K.V. Indukaev and V.A. Andreev

AMPHORA Laboratories, Moscow, Russia

The action principle and design of phase interferometric microscopy are described. The criteria set with the help of which one can estimate the device’s potentialities is formulated. The interferometric microscop constructs a phase portrait of an object under investigation. The form of this portrait depends on polarization of the light. Some typical examples are presented and analyzed. It is shown that in order to find real geometric form of the object in some special cases one must use topological phases. First of all the Rytov-Vladimirski and Pancharantnam phases. With their help one can find its optical material parameters, for example the distribution of reflection and refraction coefficients on the surface of the object under investigation..

 

Protein-based quantum computation
Part 1. Cytochromes and nanoparticles for electronic QC

C. Nicolini, E. Pechkova, V. Sivozhelezov

Apart from the disputed issue of qubits in protein systems and their biological significance [1], proteins have highly specific and stable nanometer-scale 3D structures, easy to manipulate using biotechnology. We investigated the viability of such structures as matrices for positioning the qubits, the latter being a semiconductor nanoparticle (quantum dot), a metal ion, or an organic molecule intrinsically present in some proteins (prosthetic group). For a protein with an iron porphyrin (heme) prosthetic group, Cytochrome P450scc, we have shown that highly ordered 2D structures can be obtained using LB film technology [2], that their behavior can be modeled using cellular automata [3], and that the electronic properties of the heme can be modulated using mutagenesis [4]. This shows a great inherent potential of proteins as 'guiding template' for the construction of one and two dimensional nanoarrays of nanoparticles [5] thereby controlling spatial arrangements of qubits in a quantum computer, particularly if combined by nanotechnology for providing the nanocontacts allowing to electrically address single molecules [6], which is crucial in view of the pressing task of developing qubit-based "subprocessor" combined with classical control and readout in a single device [7]. We also simulated the protein matrix by organic chemistry and have shown significant ordering for CdS quantum dots in arachidate based LB films, for which moreover distinct single electron behavior was observed [8], TiO2 nanoparticles in the ionomer thin films [9], and even aggregated layers of CuS films [10], which again confirms the necessity of an integrated protein nanobiotechnology approach to quantum computing.

[1] Hameroff S., Nip A., Porter M., Tuszynski J. Conduction pathways in microtubules, biological quantum computation, and consciousness. Biosystems 64:149-168 (2002); Mershin A., Kolomenski A.A., Schuessler H.A., Nanopoulos D.V. Tubulin dipole moment, dielectric constant and quantum behavior: computer simulations, experimental results and suggestions. Biosystems 77:73-85 (2004).

[2] Paternolli C., Antonini M., Ghisellini P., Nicolini C., Recombinant cytochrome P450 immobilization for biosensor application, Langmuir 20:11706-11712 (2004)

[3] Nicolini C., Vinciarelli A., Sivozhelezov V. Towards computational nanotechnology based on protein automata. abstract for a presentation given at the Sixth Foresight Conference on Molecular Nanotechnology. http://www.foresight.org/Conferences/MNT6/Abstracts/Nicolini/index.html (1997)

[4] Sivozhelezov V., Nicolini C. Homology modeling of cytochrome P450scc and the mutations for optimal amperometric sensor, Journal of Theoretical Biology 234:479-485 (2005)

[5] Pechkova E., Nicolini C. In: Proteomics And Nanocrystallography, Boston/Dordrecht/London: Kluwer, p.168 (2004).

[6] Carrara S., Riley D. J., Bavastrello V., Stura E., Nicolini C. Methods to fabricate nanocontacts for electrical addressing of single molecules. Sensors and Actuators B 105:542-548 (2005)

[7] US Government Advanced Research and Development Activity, QIST Quantum Computing Roadmap, Overview, p.12, http://qist.lanl.gov, 2004

[8] Facci P., Erokhin V., Carrara S., Nicolini C. Room temperature single-electron junction, Proceeding National Academy of Sciences USA 93:10556-10559 (1996)

[9] Bertoncello P., Notargiacomo A., Nicolini C. Langmuir-Schaefer Films of Nafion with incorporated TiO2 nanoparticles, Langmuir 21:172-177 (2005)

[10] Erokhina S., Erokhin V., Nicolini C., Sbrana F., Ricci D., Di Zitti E. Microstructure origin of the conductivity difference in aggregated CuS films of different thickness, Langmuir 19:766-771 (2003)

 

Protein-based quantum computation
Part 2. Possible use of rhosopsins as efficient optical QC detectors

V. Sivozhelezov, C. Nicolini

Optical implementations of qubits was successfully applied in a wide range of theoretical and experimental quantum computation research, as well as applications, due to intrinsic lack of decoherence and ability for high precision control [1]. However, highly efficient single-photon detectors are required for displaying the result of optical QC because of the extremely small photon-photon coupling available in existing materials [2]. The visual membranes of higher biological organisms easily captures single photons [3], while in some biological species they also capture the polarization of light [4], the latter being the signal-encoding parameter in optical QC. We investigate the possible use of rhodopsins, the main component of visual membranes, as a material for photonic qubit detector [5], and show that the use of nanobiotechnology can allow high-precision manipulation of the light acceptor, retinal, including converting its surrounding into that of bacterial rhodopsin (BR). Previously, we used BR for photovoltaic cells showing single photon response of BR based materials [6,7]. We also proved the viability of BR as a light-addressable transducer [8]. Besides, BR was already used in optical-computation devices [9] as well as in optical data storage and data encryption [10]. Rhodopsin can therefore be used to obtain multicomponent and highly regular 2D structures with a high potential for being efficient optical QC detectors.

[1] US Government Advanced Research and Development Activity, QIST Quantum Computing Roadmap, Overview, p.12, http://qist.lanl.gov (2004)

[2] Duan L.M., Kimble H.J. Scalable photonic quantum computation through cavity-assisted interactions. Phys Rev Lett. 92:127902 (2004)

[3] Field G.D., Sampath A.P., Rieke F. Retinal processing near absolute threshold: from behavior to mechanism. Annu Rev Physiol. 67:491-514 (2005)

[4] Shashar N., Cronin T.W. Polarization contrast vision in Octopus. J Exp Biol. 199: 999 1004 (1996)

[5] Sivozhelezov V., Nicolini C. Homology model of octopus rhodopsin: comparison with bacteriorhodopsin structure towards theoretical framework for octopus rhodopsin crystallization and function grafting from bacteriorhodopsin, pending (2005)

[6] Bertoncello P., Nicolini D., Paternolli C., Bavastrello V., Nicolini C. Bacteriorhodopsin-based Langmuir-Schaefer films for solar energy capture. IEEE Transactions on Nanobioscience 2:124 132 (2003)

[7] Nicolini C., Erokhin V., Paddeu S., Paternolli C., Ram M.K. Toward bacteriorhodopsin based photocells. Biosensors & Bioelectronics 14:427-433 (1999)

[8] Nicolini C., Erokhin V., Paddeu S., Sartore M. Towards light-addressable transducer bacteriorhodopsin based, Nanotechnology 9:223-227 (1998)

[9] Lewis A., Albeck A., Lange Y., Benchowski J., Weizman G. Optical Computation with Negative Light Intensity with a Plastic Bacteriorhodopsin Film. Science 275:1462-1464 (1997)

[10] Hampp N. Bacteriorhodopsin as a Photochromic Retinal Protein for Optical Memories. Chem Rev. 100:1755-1776 (2000)