Pairwise correlations via quantum discord and its geometric measure in a four-qubit spin chain

The dynamic of pairwise correlations, including quantum entanglement (QE) and discord (QD) with geometric measure of quantum discord (GMQD), are shown in the four-qubit Heisenberg XX spin chain. The results show that the effect of the entanglement degree of the initial state on the pairwise correlations is stronger for alternate qubits than it is for nearest-neighbor qubits. This parameter results in sudden death for QE, but it cannot do so for QD and GMQD. With different values for this entanglement parameter of the initial state, QD and GMQD differ and are sensitive for any change in this parameter. It is found that GMQD is more robust than both QD and QE to describe correlations with nonzero values, which offers a valuable resource for quantum computation.     

Remote control of quantum correlations in a two-qubit receiver by a three-qubit sender

We study remote control of quantum correlations (discord) in a subsystem of two qubits (receiver) via parameters of the initial state of another three-qubit subsystem (sender) connected to the receiver by an inhomogeneous spin s = 1/2 chain. We propose two parameters characterizing the creatable correlations. The first parameter is the discord between the receiver and the remainder of the spin s = 1/2 chain, and it concerns the mutual correlations between these two subsystems. The second parameter is the discord between the two nodes of the receiver and describes the inner correlations of the receiver. We study the dependence of these two discords on the inhomogeneity parameter of the spin chain.     

Quantum and classical correlations in high-temperature dynamics of two coupled large spins

We study the dynamical correlations between two coupled spins depending on time and the value of the spin quantum numbers. In the high-temperature approximation, we obtain analytic expressions for the mutual information and the quantum and classical parts of correlations. We consider both orthogonal and nonorthogonal measurements in the basis of spin coherent states. We show that at small times, the quantum part of correlations becomes much less than the classical part as the spin quantum numbers increase, while the situation is quite different at times equal to half the quantum period.     

Quantum teleportation

In the framework of an algebraic approach, we consider a quantum teleportation procedure. It turns out that using the quantum measurement nonlocality hypothesis is unnecessary for describing this procedure. We study the question of what material objects are information carriers for quantum teleportation. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 1, pp. 79–98, October, 2008.     

Properties of 1D Classical and Quantum Ising Models: Rigorous Results

In this paper, we consider one-dimensional classical and quantum spin-1/2 quasi-periodic Ising chains, with two-valued nearest neighbor interaction modulated by a Fibonacci substitution sequence on two letters. In the quantum case, we investigate the energy spectrum of the Ising Hamiltonian, in presence of constant transverse magnetic field. In the classical case, we investigate and prove analyticity of the free energy function when the magnetic field, together with interaction strength couplings, is modulated by the same Fibonacci substitution (thus proving absence of phase transitions of any order at finite temperature). We also investigate the distribution of Lee–Yang zeros of the partition function in the complex magnetic field regime, and prove its Cantor set structure (together with some additional qualitative properties), thus providing a rigorous justification for the observations in some previous works. In both, quantum and classical models, we concentrate on the ferromagnetic class.     

Quantum correlation with entanglement and mutual entropy

We discuss the correlations on classical and quantum systems from the information theoretical points of view. There exists an essential difference between such two types of correlation. How can we understand such difference? This report is a review of our recent works on the quantum information theory with entanglement.     

Quantum Macroscopic Effects in a Degenerate Strongly Magnetized Nucleon Gas

A model of a degenerate gas consisting of neutrons that are in chemical equilibrium with degenerate protons and electrons in a stationary and homogeneous superstrong magnetic field is used to describe the state of the matter in central regions of strongly magnetized neutron stars. Expressions for thermodynamic quantities (such as energy density, particle density, pressure, and magnetization) characterizing a degenerate gas of neutrons, protons, and electrons are obtained. In these expressions, the contributions determined by the interaction between anomalous magnetic moments of fermions and the magnetic field are taken into account. Macroscopic effects that may occur in strongly magnetized neutron stars are discussed. We show that all thermodynamic quantities characterizing electrically charged fermions in a strong magnetic field are subject to nonperiodic oscillations caused by the interaction of the anomalous magnetic moments of protons and electrons with the magnetic field. We also show that if the nucleon density and the electron density exceed threshold values that are relatively small and depend on the magnetic field strength, all fermions are fully polarized with respect to the spin. The full spin polarization effect in neutrons is caused by the interaction between the anomalous magnetic moment and the magnetic field. The obtained results may prove useful in understanding processes that occur in the nucleus of a neutron star with a magnetic field frozen into the star.     

Vanishing quantum discord and complete entropy exchange between subsystems in a bipartite system

Vanishing quantum discord and the entropy correlations between subsystems in a bipartite system are investigated. We numerically verify that there exists a condition of complete entropy exchange between the two subsystems, and it is found that the condition is in excellent agreement with that of the nullity of quantum discord in a certain range of parameters of the bipartite system.     

Local Thermal Equilibrium States and Quantum Energy Inequalities

In this paper we investigate the energy distribution of states of a linear scalar quantum field with arbitrary curvature coupling on a curved spacetime which fulfill some local thermality condition. We find that this condition implies a quantum energy inequality for these states, where the (lower) energy bounds depend only on the local temperature distribution and are local and covariant (the dependence of the bounds other than on temperature is on parameters defining the quantum field model, and on local quantities constructed from the spacetime metric). Moreover, we also establish the averaged null energy condition (ANEC) for such locally thermal states, under growth conditions on their local temperature and under conditions on the free parameters entering the definition of the renormalized stress-energy tensor. These results hold for a range of curvature couplings including the cases of conformally coupled and minimally coupled scalar field. Submitted: February 27, 2008. Accepted: May 5, 2008.     

基于异质预期的量子伯川德博弈复杂动力机制分析

针对伯川德双寡头垄断博弈经济系统中出现的混沌现象,利用量子博弈论,构建了基于有限理性与天真预期行为的量子伯川德动态博弈模型,分析了量子纠缠度对纳什均衡点稳定性及复杂动力行为的影响。结果表明:量子纠缠度能增强该系统的稳定性,企业价格调整速度达到某一程度时会导致该系统的复杂混沌特性,纠缠度可以有效控制混沌状态。最后利用数值模拟从分岔、最大李雅普诺夫指数、奇怪吸引子、初始条件敏感性及分数维数方面验证了理论准确性。     

Separability and entanglement in tripartite states

While classical correlations can be freely distributed among many systems, this is not true for entanglement and quantum correlations. If a quantum system S^a is entangled with another quantum system S^b, then its entanglement with any third quantum system S^c cannot be arbitrary. This is the celebrated monogamy of entanglement. Implicit in this general statement is the plausible belief that only entanglement between the systems S^a and S^b constrains the entanglement between S^a and the third system S^c. We demonstrate that even classical correlations between S^a and S^b may impose surprisingly stringent restrictions on the possible entanglement between S^a and S^c. In particular, perfect bipartite classical correlations and full entanglement cannot coexist in any tripartite state. An intuitive explanation of this monogamy of hybrid classical and quantum correlations might be that the system S^a has a correlating capability, which cannot be used to establish any entanglement with a third system (but can still be used to establish classical correlations) if it is exhausted when correlated with S^b (in either a classical or quantum fashion). This may be interpreted as an alternate version of monogamy.     

Correlation and Entanglement

In quantum mechanics, it is long recognized that there exist correlations between observables which are much stronger than the classical ones. These correlations are usually called entanglement, and cannot be accounted for by classical theory. In this paper, we will study correlations between observables in terms of covariance and the Wigner-Yanase correlation, and compare their merits in characterizing entanglement. We will show that the Wigner-Yanase correlation has some advantages over the conventional covariance.     

On the Spectrum of 1D Quantum Ising Quasicrystal

We consider one-dimensional quantum Ising spin-1/2 chains with two-valued nearest neighbor couplings arranged in a quasi-periodic sequence, with uniform, transverse magnetic field. By employing the Jordan–Wigner transformation of the spin operators to spinless fermions, the energy spectrum can be computed exactly on a finite lattice. By employing the transfer matrix technique and investigating the dynamics of the corresponding trace map, we show that in the thermodynamic limit the energy spectrum is a Cantor set of zero Lebesgue measure. Moreover, we show that local Hausdorff dimension is continuous and non-constant over the spectrum. This forms a rigorous counterpart of numerous numerical studies.     

Entanglement measures based on observable correlations

By regarding quantum states as communication channels and using observable correlations quantitatively expressed by mutual information, we introduce a hierarchy of entanglement measures that includes the entanglement of formation as a particular instance. We compare the maximal and minimal measures and indicate the conceptual advantages of the minimal measure over the entanglement of formation. We reveal a curious feature of the entanglement of formation by showing that it can exceed the quantum mutual information, which is usually regarded as a theoretical measure of total correlations. This places the entanglement of formation in a broader scenario, highlights its peculiarity in relation to pure-state ensembles, and introduces a competing definition with intrinsic informational significance. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 3, pp. 453–462, June, 2008.     

Quantum Scattering in a Periodically Pulsed Magnetic Field

In this paper, we study the quantum dynamics of a charged particle in the plane in the presence of a periodically pulsed magnetic field perpendicular to the plane. We show that by controlling the cycle when the magnetic field is switched on and off appropriately, the result of the asymptotic completeness of wave operators can be obtained under the assumption that the potential V satisfies the decaying condition \({|V(x)| \le C(1 + |x|)^{-\rho}}\) for some \({\rho > 0}\).     

Natural atomic probabilities in quantum information theory

Quantum Information Theory has witnessed a great deal of interest in the recent years since its potential for allowing the possibility of quantum computation through quantum mechanics concepts such as entanglement, teleportation and cryptography. In Chemistry and Physics, von Neumann entropies may provide convenient measures for studying quantum and classical correlations in atoms and molecules. Besides, entropic measures in Hilbert space constitute a very useful tool in contrast with the ones in real space representation since they can be easily calculated for large systems. In this work, we show properties of natural atomic probabilities of a first reduced density matrix that are based on information theory principles which assure rotational invariance, positivity, and N- and v-representability in the Atoms in Molecules (AIM) scheme. These (natural atomic orbital-based) probabilities allow the use of concepts such as relative, conditional, mutual, joint and non-common information entropies, to analyze physical and chemical phenomena between atoms or fragments in quantum systems with no additional computational cost. We provide with illustrative examples of the use of this type of atomic information probabilities in chemical process and systems.     

Pauli isotonic oscillatorwith an anomalous magnetic moment in the presence of the Aharonov–Bohm effect: Laplace transform approach

A strong magnetic field significantly affects the intrinsic magnetic moment of fermions. In quantum electrodynamics, it was shown that the anomalous magnetic moment of an electron arises kinematically, while it results from a dynamical interaction with an external magnetic field for hadrons (proton). Taking the anomalous magnetic moment of a fermion into account, we find an exact expression for the boundstate energy and the corresponding eigenfunctions of a two-dimensional nonrelativistic spin-1/2 harmonic oscillator with a centripetal barrier (known as the isotonic oscillator) including an Aharonov–Bohm term in the presence of a strong magnetic field. We use the Laplace transform method in the calculations. We find that the singular solution contributes to the phase of the wave function at the origin and the phase depends on the spin and magnetic flux.     

Fractional revival and association schemes

Fractional revival occurs between two vertices in a graph if a continuous-time quantum walk unitarily maps the characteristic vector of one vertex to a superposition of the characteristic vectors of the two vertices. This phenomenon is relevant in quantum information in particular for entanglement generation in spin networks. We study fractional revival in graphs whose adjacency matrices belong to the Bose–Mesner algebra of association schemes. A specific focus is a characterization of balanced fractional revival (which corresponds to maximal entanglement) in graphs that belong to the Hamming scheme. Our proofs exploit the intimate connections between algebraic combinatorics and orthogonal polynomials.