The
Einstein-Podolsky-Rosen paradox is resolved dynamically by using spin-dependent
quantum trajectories inferred from Dirac’s equation for a relativistic
electron. The theory provides a practical computational methodology for
studying entanglement versus disentanglement for realistic Hamiltonians.

A spin-dependent quantum trajectory methodology is outlined which achieves electron exchangecorrelation on an ab initio basis. The methodology is intended to give workers in electronic structure the same computational capability which has been available for decades in classical dynamics.

Abstract:
It is shown that a single-particle wave function Ψ, obtained (Landau, 1930) as a solution of the Schr?dinger equation (for a charged particle in a homogeneous magnetic field), and an operator relation of？(or equation？) lead to the dynamic description of one-dimensional many-particle quantum filamentary states. Thus, one can overcome the problem, connected with the finding of many-body wave function as solution of the Schr?dinger equation with a very tangled Hamiltonian for multi-body system. An effect of nonlocality appears. The dependence of the linear density of particles on the magnetic field and on the number of particles in the one- dimension filamentary multiparticle quantum structure is calculated.

Abstract:
Exact
quasi-classical asymptotic beyond WKB-theory and beyond Maslov canonical
operator to the Colombeau solutions of
the n-dimensional Schrodinger equation is presented. Quantum jumps
nature is considered successfully. We pointed out that an explanation of quantum
jumps can be found to result from Colombeau solutions of the Schrodinger
equation alone without additional postulates.

With
local realism quantum mechanics established, we can simply describe an
extranuclear electron as a large-scale elastic ring with an elastic phase
trajectory. Several small molecules can thus be strictly calculated through the
logical method of establishing an accurate mechanical equilibrium equation
describing the molecular structure, then solving the strict solutions of this
mechanical equation and the corresponding wave equation. The results (bond
length and dissociation energy) are in good agreement with observed results—i.e. if it is only coincidence, there
should not be such a high probability of agreement between calculated and
observed results. The method of local realism quantum mechanics is no longer
the semi-empirical method. The method to calculate the electron pairing energy
uses a linear regression of the ionization energy obtained through experiment.
Nonetheless, it is exciting that there are diatomic molecules such as Na_{2},
K_{2} and asymmetric HF molecules that possess a non-zero non-bonding
electron number in the calculation examples. Moreover, the molecular structures
are very intuitive, and the calculation method is much simpler than existing
methods.

Abstract:
We consider a model consisting of three two-level atoms in a heavily damped cavity. We show that the quantum-jump-based feedback can be used to generate a steady entangled state of three atoms against decoherence. When the feedback acts on just one of the atoms, it can protect a maximally entangled state of other two atoms. When the feedback acts on three atoms, by choosing appropriate parameters we can obtain a decoherence-free subspace spanned by two vectors, and by using quantum trajectory Monte Carlo wave function method we find that the maximally entangled state of three atoms in this decoherence-free subspace can be obtained for some specific initial conditions.

Abstract:
A modified de Broglie--Bohm approach is generalized to the Schwarzschild black hole. By using this method, the quantum potential and the quantum trajectories of the black hole are investigated. And we find that the linear combination of two particular solutions of the black hole wavefunction is not physical although each of them is physical, if we think that the quantum gravity should reduce into its corresponding classical counterpart in which the gravity vanishes. It seems to confirm the argument, given by Alwis and MacIntire, that a possible resolution on the quantum gravity is to give up the superposition principle.

Abstract:
In a physical system, phase point trajectory is impossible to be space-filling curve, of which the dimension is not greater than one. Equipotential map concept is proposed. When phase point trajectory dimension is 0, calculus tool is no longer applicable. System state can be changed instantly. When phase point trajectory dimension is 1, differential equation can be used to handle this case.

Abstract:
The 5-qubit quantum computer prototypes that IBM has
given open access to on the cloud allow the implementation of real experiments
on a quantum processor. We present the results obtained in five experimental
tests performed on these computers: dense coding, quantum Fourier transforms,
Bell’s inequality, Mermin’s inequalities (up to n=5) and the construction of the prime state . These results serve to assess the functioning of
the IBM 5Q chips.

Abstract:
This
paper proposes the continuous controller design method for quantum Shannon
entropy, which can continuously drive the entropy to track a desired
trajectory. We also analyzed the controllability of Shannon entropy in very
short time interval. Simulations are done on five dimensional quantum system,
which can verify the validation of the method.