Contents of the Proceedings of the 11th International Colloquium on Quantum Groups “Quantum Groups and Integrable Systems”

Table of Contents

Contents of the Proceedings of the 11th International Colloquium on Quantum Groups Quantum Groups and Integrable Systems     

Certain Properties of a Quantum Information Network Driven by External Fields

A quantum information network with the structure of the property and information characteristic is studied. Under Gaussian channel is proposed. The network topological the catastrophic and exponential external field driving, the degree distribution has the spatial and temporal characteristics, and the positive or negative power index appears, which can influence the assortativity coefficient. This is possibly helpful to open a way to using the different type of driving to introduce the expected properties for the network.     

Global Estimates of Errors in Quantum Computation by the Feynman–Vernon Formalism

The operation of a quantum computer is considered as a general quantum operation on a mixed state on many qubits followed by a measurement. The general quantum operation is further represented as a Feynman–Vernon double path integral over the histories of the qubits and of an environment, and afterward tracing out the environment. The qubit histories are taken to be paths on the two-sphere \(S^2\) as in Klauder’s coherent-state path integral of spin, and the environment is assumed to consist of harmonic oscillators initially in thermal equilibrium, and linearly coupled to to qubit operators \(\hat{S}_z\). The environment can then be integrated out to give a Feynman–Vernon influence action coupling the forward and backward histories of the qubits. This representation allows to derive in a simple way estimates that the total error of operation of a quantum computer without error correction scales linearly with the number of qubits and the time of operation. It also allows to discuss Kitaev’s toric code interacting with an environment in the same manner.     

Quantum fluctuations of the “Copenhagen vacuum”

The effective energy of the approximate gauge-field configuration customarily known as the Copenhagen vacuum is calculated in the single-loop approximation. It is shown that this quantity is always positive and so it is impossible to make any statements about the spontaneous generation of such a field. The possibility of the temperature stabilization of a homogeneous chromomagnetic field is also discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 74–79, May, 1986.     

Network breakdown “at the edge of chaos” in multi-agent traffic simulations

Traffic is highly influenced by network structure and human behaviour. Small changes in the human behaviour can lead to huge changes in the load of a traffic network. Current transportation models do not, and most of them cannot, research such random behaviour but always calculate a steady state. In our multi-agent transport simulation, we frequently observe seemingly random “network breakdowns”, huge traffic jams that spread over a big part of the network, making a normal traffic flow impossible. This paper describes the investigations that were performed on the results of our large-scale multi-agent transport simulations in an attempt to contribute to the better understanding of the dynamic processes in such simulations and, hopefully, better understanding and modelling of the real-world.     

Improvement of the Hopfield Neural Network by MC-Adaptation Rule

We show that the performance of the Hopfield neural networks, especially the quality of the recall and the capacity of the effective storing, can be greatly improved by making use of a recently presented neural network designing method without altering the whole structure of the network. In the improved neural network, a memory pattern is recalled exactly from initial states having a given degree of similarity with the memory pattern, and thus one can avoids to apply the overlap criterion as carried out in the Hopfield neural networks.     

Separability of Pure and Mixed States of the Quantum Network of Four Nodes

This article discusses the separability of the pure and mixed states of the quantum network of four nodes by means of the criterion of entanglement in terms of the covariance correlation tensor in quantum network theory.     

Quantum Logic Network for Probabilistic Teleportation of Two-Particle State in a General Form

A simplification scheme of probabilistic teleportation of two-particle state in a general form is given.By means of the primitive operations consisting of single-qubit gates,two-qubit controlled-not gates,Von Neumann measure-ment and classically controlled operations,we construct and efficient quantum logical network for implementing the new scheme of probabilistic teleportation of a two-particle state in a general form.     

Comment on “Quantum discord through the generalized entropy in bipartite quantum states”

In [X.-W. Hou, Z.-P. Huang, S. Chen, Eur. Phys. J. D 68, 87 (2014)], Hou et al. present, using Tsallis’ entropy, possible generalizations of the quantum discord measure, finding original results. As for the mutual informations and discord, we show here that these two types of quantifiers can take negative values. In the two qubits instance we further determine in which regions they are non-negative. Additionally, we study alternative generalizations on the basis of Rényi entropies.     

Bipartite Entanglement in the Two-Mode Quantum Kicked Top

We show that the bipartite entanglement in the two-mode quantum kicked top can reveal the underlying chaotic and regular structures in phase space： namely, the entanglement displays a rapid rise after a very short time for an initial spin coherent state centred in a chaotic region of the phase space, whereas the entanglement displays a periodic modulation for the coherent state centred at an elliptic fixed point. The quantum-classical correspondence is investigated by studying the mean and maximal linear entropy.     

Unreasonable and “Unreasonable” in Quantum Mechanics?

The particles of quantum mechanics (QM) are discrete undulatory entities which are described in terms of the complex state vectors of the theory in full agreement with experiment. The wave-particle paradox stems from the fact that undulation and discreteness are inconsistent within the classical theory which was historically the point of departure for the canonical foundation. The author describes his prolonged efforts of anchoring the state vector of QM in experiment rather in obsolete theory.     

Quantum beats in the 3γ annihilation decay of Positronium observed by perturbed angular distribution

We have applied conventional Time Differential Perturbed Angular Correlation (TDPAC) method to observe the anisotropy oscillations in the 3γ annihilation decay of polarized Positronium in a weak magnetic field. The effect, as predicted theoretically and experimentally demonstrated by Barishevsky et al. [V.G. Barishevsky, O.N. Metelitsa, V.V. Tikhomirov, Oscillations of the positronium decay γ-quantum angular distribution in a magnetic field, J. Phys. B: At. Mol. Opt. Phys.22 (1989) 2835], is induced by the coherent admixture of the m = 0 states of ortho-Positronium (o-Ps) and para-Positronium (p-Ps) in interaction with the magnetic field.The following experimental characteristics are to be considered:

(i)

the oscillation frequency corresponds to the difference in energy of the Ps atom levels in magnetic field and is proportional with H²;

(ii)

in a fixed geometry the modulation depth (oscillations amplitude) depends on the mean positron polarization;

(iii)

privileged angles of the polarization vector, magnetic field and detectors are required for optimizing the observed oscillations amplitude.

The normalized difference spectrum function (R(t)) obtained from time spectra measured in vacuum and in different gaseous atmospheres (Ar, H₂, N₂) have the oscillations amplitude constant and we conclude that the Ps atoms are not fully thermalized over a time interval of about 400 ns.The R(t) functions obtained for o-Ps annihilation decays, in dry air or Ar-O mixture, have the oscillations amplitude time dependent due, probably, to the paramagnetism of the Oxygen molecules.     

Implement of FEC in the Optical Transport Network

Forward error correction (FEC) is a method by which extra information is included along with the original signal to provide redundancy for correcting bit errors. According to Reed Solomon code regularity, a certain amount of bit errors can be corrected. The appropriate capability of correcting burst bits in error may be more flexible implement of FEC in the optical transport network. The suitable choice can effectively reduce cost of the optical transport network.     

A Decoherence-Reduction Scheme by Waveguides in Quantum Information Processing

Based on the result of cavity quantum electrodynamics, we suggest a method, in which the Fabry-Perot cavity or the confocal cavity is replaced by a waveguide with the size comparable to the wavelength of the photon, to reduce decoherence caused by spontaneous emission in quantum information processing, especially in the realization of quantum computation. Since a waveguide has a lowest cutoff frequency while a Fabry-Perot cavity or a confocal cavity has none, the spontaneous emission of excited atoms will be forbidden in an ideal waveguide with an appropriate size. To avoid the influence of the non-ideal conducting walls on the atom in a realistic waveguide, which will lead to decoherence, we suggest that the waveguide should be coated by a thin film of transparent insulating medium. In our method, the quantum information is represented by a multi-level atom or molecule; any two of its levels can be used to represent a qubit in principle. Our method greatly extends the choice of the material to be used in the realization of quantum computation, and it can be used in most schemes to reduce the decoherence caused by spontaneous emission.     

Observation of Quantum Beat in Rb by Parametric Four-Wave Mixing

Two coupled paralnetric four-wave-mixing processes in Rb atoms are studied using perturbation theory, which reveals clear evidence of tile appearance of quantum beat at 608cm^-1, corresponding to the energy difference of the 7s - 5d states of Rb atoms, in the parametric four-wave-mixing signals. A pump-probe technique is utilized to observe the quantum beat. Tinle-varying characteristics of the quantum beat are investigated using time-dependellt Fourier transform. The results show that the time-varying characteistics of the quantum beat not oldy offers a sensitive detecting method for observing the decay of atomic wave packets, but also provides a potential tool for monitoriHg the dissociation of molecules.     

Can Quantum Gravity be Exposed in the Laboratory?

I propose an experiment that may be performed, with present low temperature and cryogenic technology, to reveal Wheeler’s quantum foam. It involves coupling an optical photon’s momentum to the center of mass motion of a macroscopic transparent block with parameters such that the latter is displaced in space by approximately a Planck length. I argue that such displacement is sensitive to quantum foam and will react back on the photon’s probability of transiting the block. This might allow determination of the precise scale at which quantum fluctuations of space–time become large, and so differentiate between the brane-world and the traditional scenarios of spacetime.