The effect and control on remaining the quantum correlation by the coupling symmetry between qubits and the bath

We study the dynamic evolution of quantum correlation of two interacting coupled qubits system in non-Markov environment, and quantify the quantum correlation using concurrence and quantum discord. We find that although both of them are physical quantities which measure the system characteristics of the quantum correlations, the quantum discord is more robust than concurrence, since it can keep a positive value even when the ESD happens. The quantum correlation of quantum system not only depends on the initial state but also strongly depends on the coupling ways between qubits and environment. For the given initial state, by keeping the coupling between qubits and environment in completely symmetric, we can completely avoid the effect the decoherence influenced on the quantum correlation and effectively prolong the survival time of quantum discord and concurrence. We also find that the stronger the interaction between qubits is, the more conducive the death of the quantum correlation is resisted.     

Prequantum Classical Statistical Field Theory: Complex Representation, Hamilton-Schrödinger Equation, and Interpretation of Stationary States

We develop a prequantum classical statistical model in that the role of hidden variables is played by classical (vector) fields. We call this model Prequantum Classical Statistical Field Theory (PCSFT). The correspondence between classical and quantum quantities is asymptotic, so we call our approach asymptotic dequantization. We construct the complex representation of PCSFT. In particular, the conventional Schrödinger equation is obtained as the complex representation of the system of Hamilton equations on the infinite-dimensional phase space. In this note we pay the main attention to interpretation of so called pure quantum states (wave functions) in PCSFT, especially stationary states. We show, see Theorem 2, that pure states of QM can be considered as labels for Gaussian measures concentrated on one dimensional complex subspaces of phase space that are invariant with respect to the Schrödinger dynamics. “A quantum system in a stationary state ψ” in PCSFT is nothing else than a Gaussian ensemble of classical fields (fluctuations of the vacuum field of a very small magnitude) which is not changed in the process of Schrödinger's evolution. We interpret in this way the problem of stability of hydrogen atom. One of unexpected consequences of PCSFT is the infinite dimension of physical space on the prequantum scale.     

Quantum integrability is not a trivial consequence of classical integrability

We discuss the construction of quantum mechanical commuting quantities when the classical ones are known. It is shown that the simple correspondence rules proposed so far do not always work. A candidate for a classically integrable quantum mechanically nonintegrable two-dimensional system is given.     

Dynamical learning of non-Markovian quantum dynamics

We study the non-Markovian dynamics of an open quantum system with machine learning.The observable physical quantities and their evolutions are generated by using the neural network.After the pre-training is completed,we fix the weights in the subsequent processes thus do not need the further gradient feedback.We find that the dynamical properties of physical quantities obtained by the dynamical learning are better than those obtained by the learning of Hamiltonian and time evolution operator.The dynamical learning can be applied to other quantum many-body systems,non-equilibrium statistics and random processes.     

Quantum correlations from local amplitudes and the resolution of the Einstein-Podolsky-Rosen nonlocality puzzle

The Einstein-Podolsky-Rosen (EPR) nonlocality puzzle has been recognized as one of the most important unresolved issues in the foundational aspects of quantum mechanics. We show that the problem is more or less entirely resolved, if the quantum correlations are calculated directly from local quantities, which preserve the phase information in the quantum system. We assume strict locality for the probability amplitudes instead of local realism for the outcomes and calculate an amplitude correlation function. Then the experimentally observed correlation of outcomes is calculated from the square of the amplitude correlation function. Locality of amplitudes implies that measurement on one particle does not collapse the companion particle to a definite state. Apart from resolving the EPR puzzle, this approach shows that the physical interpretation of apparently “nonlocal” effects, such as quantum teleportation and entanglement swapping, are different from what is usually assumed. Bell-type measurements do not change distant states. Yet the correlations are correctly reproduced, when measured, if complex probability amplitudes are treated as the basic local quantities. As examples, we derive the quantum correlations of two-particle maximally entangled states and the three-particle Greenberger-Horne-Zeilinger entangled state.     

The structure of quantum fluids

We outline the principal features of Bose and Fermi fluids that are revealed in particle scattering experiments at high momentum transfer. In this regime, the dynamic structure function is determined by the dominant influence of correlations which are embodied in the static one- and two-body density matrices characterizing a strongly correlated system. We analyze the general structure of these fundamental quantities and of the associated momentum distributions that enter as input quantities for determining the dynamical response. We discuss their physical interpretation and their interrelationships. We further describe the main features of advanced many-body methods, which begin on a nonperturbative basis. They permit a formal and numerical evaluation of various quantities that characterize the structure of the density matrices and therewith of quantum fluids and solids.Dedicated to Peter Mittelstaedt on the occasion of his sixtieth birthday.     

Condition for any realistic theory of quantum systems

In quantum physics, the density operator completely describes the state. Instead, in classical physics the mean value of physical quantities is evaluated by means of a probability distribution. We study the possibility to describe pure quantum states and events with classical probability distributions and conditional probabilities and prove that the distributions have to be nonlinear functions of the density operator. Some examples are considered. Finally, we deal with the exponential complexity problem of quantum physics and introduce the concept of classical dimension for a quantum system.     

On generally covariant quantum field theory and generalized causal and dynamical structures

We give an example of a generally covariant quasilocal algebra associated with the massive free field. Maximal, two-sided ideals of this algebra are algebraic representatives of external metric fields. In some sense, this algebra may be regarded as a concrete realization of Ekstein's ideas of presymmetry in quantum field theory. Using ideas from our example and from usual algebraic quantum field theory, we discuss a generalized scheme, in which maximal ideals are viewed as algebraic representatives of dynamical equations or Lagrangians. The considered frame is no quantum gravity, but may lead to further insight into the relation between quantum theory and space-time geometry.     

Schwarzschild geometry,once more

Schwarzschild geometry exhibits interesting features when the field equations are decomposed with respect to a system of freely falling observers. We only use quantities behaving like tensors under a restricted group of transformations of the reference system. Moreover Lorentz transformations with non-constant velocities drastically change the physical picture of the theory.     

Quantum Integrable Toda-Like Systems in Deformation Quantization

We define and discuss the notion of quantum integrability of a classically integrable system within the framework of deformation quantization, i.e. the question whether the classical conserved quantities (which are already in involution with respect to the Poisson bracket) commute with respect to some star product on the phase space after possible quantum corrections. As an example of this method, we show by means of suitable 2 by 2 quantum R-matrices that a list of Toda-like classical integrable systems given by Y. B. Suris is quantum integrable with respect to the usual star product of the Weyl type in flat 2n-dimensional space.     

Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes

Searches for possible new quantum phases and classifications of quantum phases have been central problems in physics. Yet, they are indeed challenging problems due to the computational difficulties in analyzing quantum many-body systems and the lack of a general framework for classifications. While frustration-free Hamiltonians, which appear as fixed point Hamiltonians of renormalization group transformations, may serve as representatives of quantum phases, it is still difficult to analyze and classify quantum phases of arbitrary frustration-free Hamiltonians exhaustively. Here, we address these problems by sharpening our considerations to a certain subclass of frustration-free Hamiltonians, called stabilizer Hamiltonians, which have been actively studied in quantum information science. We propose a model of frustration-free Hamiltonians which covers a large class of physically realistic stabilizer Hamiltonians, constrained to only three physical conditions; the locality of interaction terms, translation symmetries and scale symmetries, meaning that the number of ground states does not grow with the system size. We show that quantum phases arising in two-dimensional models can be classified exactly through certain quantum coding theoretical operators, called logical operators, by proving that two models with topologically distinct shapes of logical operators are always separated by quantum phase transitions.     

Quantum phase transitions in matrix product states of one-dimensional spin-1 chains

We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system has three different quantum phases and by adjusting the control parameters we are able to realize any phase, any two phases equal coexistence and the three phases equal coexistence. At every critical point the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N-spin maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of certain directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-spin maximal entanglement.     

Interference Behaviors of Resonant Transport Through a Mesoscopic System with ac Responses

Time-dependent interference behaviors on currents transporting through a mesoscopic system are investigated by using the Keldysh nonequilibrium Green function technique. The system is composed of a quantum dot coupled with two electron reservoirs. The electrons in the quantum dot are perturbed by two microwave fields (MWFs) through gate. The MWFs cause the energy level splitting in the quantum dot to form multi-channel for the tunneling current, and these branches of current interfere to produce stable oscillation. The resulting oscillation of current is strongly associated with frequency relations between MWFs. The timedependent current is the consequence of resonant effects for electrons resonating with quantum dot state and with MWFs. We present numerical calculations for the cases where the Coulomb interaction U = 0. Negative temporal current and differential conductance are observed even if the dc bias is not small. We compare the results with corresponding quantities in the system perturbed by single MWF.     

A new approach to electron-electron interactions in strongly correlated systems at arbitrary spin-polarization and temperature

The uniform electron fluid is the reference model for density functional calculations. Even for this system, many-body perturbation theory, and related methods become questionable when the density parameter r_s exceeds unity. Hence, quantum Monte Carlo (QMC) simulation has been almost the only applicable method. We review a new approach, which uses a mapping of the quantum fluid to a classical Coulomb fluid, based on density-functional concepts. It is applicable at finite temperatures and arbitrary spin polarizations as well, and correctly recovers even the logarithmic terms in the exchange and correlations energies close to T=0. We show by detailed comparison with available QMC data that the method yields accurate pair-distribution functions, spin-dependent energies, static local-field factors, Landau parameter-based quantities like m∗ and g∗, for strongly coupled electron fluids.     

Intersubband transition in quantum wells and triple-barrier diode infrared detector concepts

We present effective mass theory results for intersubband transition energies, oscillator strengths, and other quantities which are relevant to the design of quantum well devices. Results are presented in the form of contour plots for easy reference. Theory gives good agreement with existing experimental data by various research groups. In addition, a new quantum well infrared detector is proposed, which employs resonant tunneling in a triple-barrier diode. The device has a narrow bandwidth controlled by the resonance width and a very low dark current making high temperature (> 77 K) operation possible.     

Application of Entangled State Representation to Deriving Normally Ordered Expansion of 1-Dimensional Coulomb Potential

Guided by Dirac’s advice that “When one has a particular problem to work out in quantum mechanics, one can minimize the labour by using a representation in which the representatives of the more important abstract quantities occurring in that problem are as simple as possible,’’ we construct the entangled state representation to derive the normally ordered expansion formula of the 1-dimensional two-body Coloumb potential. The method of integration within an ordered product of operators is also used. Further application of the new formula in some perturbation calculation is discussed.     

Transferring information through a mixed-five-spin chain channel

We initially introduce one-dimensional mixed-five-spin chain with Ising-XY model which includes mixture of spins-1/2 and spins-1. Here, it is considered that nearest spins(1, 1/2) have Ising-type interaction and nearest spins(1/2, 1/2)have both XY-type and Dzyaloshinskii–Moriya(DM) interactions together. Nearest spins(1, 1) have X X Heisenberg interaction. This system is in the vicinity of an external homogeneous magnetic field B in thermal equilibrium state. We promote the quantum information transmitting protocol verified for a normal spin chain with simple model(refer to Rossini D, Giovannetti V and Fazio R 2007 Int. J. Quantum Infor. 5 439)(widely in reference: Giovannetti V and Fazio R 2005 Phys. Rev. A 71 032314) by means of considering the suggested mixed-five-spin chain as a quantum communication channel for transmitting both qubits and qutrits ideally. Hence, we investigate some useful quantities such as quantum capacity and quantum information transmission rate for the system. Finally, we conclude that, when the DM interaction between spins(1/2, 1/2) increases the system is a more ideal channel for transmitting information.     

Pairwise correlations in a three-partite quantum system from a prequantum random field

Prequantum classical statistical field theory (PCSFT) is a model that provides the possibility to represent the averages of quantum observables (including correlations of observables on subsystems of a composite system) as averages with respect to fluctuations of classical random fields. In view of the PCSFT terminology, quantum states are classical random fields. The aim of our approach is to represent all quantum probabilistic quantities by means of classical random fields. We obtain the classical-random-field representation for pairwise correlations in three-partite quantum systems. The three-partite case (surprisingly) differs substantially from the bipartite case. As an important first step, we generalized the theory developed for pure quantum states of bipartite systems to the states given by density operators.     

Ratchet effect: demonstration of a relativistic fluxon diode

We report the observation of the ratchet effect for a relativistic flux quantum trapped in an annular Josephson junction embedded in an inhomogeneous magnetic field. In such a solid state system, mechanical quantities are proportional to electrical quantities, so that the ratchet effect represents the realization of a relativistic-flux-quantum-based diode. Mean static voltage response, equivalent to directed fluxon motion, is experimentally demonstrated in such a diode for deterministic as well as stochastic oscillating current forcing.     

Universal conductance and conductivity at critical points in integer quantum Hall systems

The sample averaged longitudinal two-terminal conductance and the respective Kubo conductivity are calculated at quantum critical points in the integer quantum Hall regime. In the limit of large system size, both transport quantities are found to be the same within numerical uncertainty in the lowest Landau band, and , respectively. In the second-lowest Landau band, a critical conductance is obtained which indeed supports the notion of universality. However, these numbers are significantly at variance with the hitherto commonly believed value . We argue that this difference is due to the multifractal structure of critical wave functions, a property that should generically show up in the conductance at quantum critical points.