Entanglement measure for general pure multipartite quantum states

We propose an explicit formula for an entanglement measure of pure multipartite quantum states, then study a general pure tripartite state in detail, and at end we give some simple but illustrative examples on four-qubits and m-qubits states.Comment: 5 page

Entanglement for a two-parameter class of states in 2⊗n2\otimes n quantum system

We exhibit a two-parameter class of states $\rho_{(\alpha,\gamma)}$, in $2\otimes n$ quantum system for $n\ge 3$, which can be obtained from an arbitrary state by means of local quantum operations and classical communication, and which are invariant under all bilateral %unitary operations %of the form $U\otimes U$ on $2\otimes n$ quantum system. We calculate the negativity of $\rho_{(\alpha,\gamma)}$, and a lower bound and a tight upper bound on its entanglement of formation. It follows from this calculation that the entanglement of formation of $\rho_{(\alpha,\gamma)}$ cannot exceed its negativity.Comment: 10 pages, including 4 figures, accepted for publication in J. Phys.

Time-of-arrival in quantum mechanics

We study the problem of computing the probability for the time-of-arrival of a quantum particle at a given spatial position. We consider a solution to this problem based on the spectral decomposition of the particle's (Heisenberg) state into the eigenstates of a suitable operator, which we denote as the ``time-of-arrival'' operator. We discuss the general properties of this operator. We construct the operator explicitly in the simple case of a free nonrelativistic particle, and compare the probabilities it yields with the ones estimated indirectly in terms of the flux of the Schr\"odinger current. We derive a well defined uncertainty relation between time-of-arrival and energy; this result shows that the well known arguments against the existence of such a relation can be circumvented. Finally, we define a ``time-representation'' of the quantum mechanics of a free particle, in which the time-of-arrival is diagonal. Our results suggest that, contrary to what is commonly assumed, quantum mechanics exhibits a hidden equivalence between independent (time) and dependent (position) variables, analogous to the one revealed by the parametrized formalism in classical mechanics.Comment: Latex/Revtex, 20 pages. 2 figs included using epsf. Submitted to Phys. Rev.

A Complete Version of the Glauber Theory for Elementary Atom - Target Atom Scattering and Its Approximations

A general formalism of the Glauber theory for elementary atom (EA) - target atom (TA) scattering is developed. A second-order approximation of its complete version is considered in the framework of the optical-model perturbative approach. A `potential' approximation of a second-order optical model is formulated neglecting the excitation effects of the TA. Its accuracy is evaluated within the second-order approximation for the complete version of the Glauber EA-TA scattering theory.Comment: PDFLaTeX, 10 pages, no figures; an updated versio

Polaron Variational Methods In The Particle Representation Of Field Theory : I. General Formalism

We apply nonperturbative variational techniques to a relativistic scalar field theory in which heavy bosons (``nucleons'') interact with light scalar mesons via a Yukawa coupling. Integrating out the meson field and neglecting the nucleon vacuum polarization one obtains an effective action in terms of the heavy particle coordinates which is nonlocal in the proper time. As in Feynman's polaron approach we approximate this action by a retarded quadratic action whose parameters are to be determined variationally on the pole of the two-point function. Several ans\"atze for the retardation function are studied and for the most general case we derive a system of coupled variational equations. An approximate analytic solution displays the instability of the system for coupling constants beyond a critical value.Comment: 33 pages standard LaTeX, 3 uuencoded gzipped postscript figures embedded with psfig.st

Experimental simulation of quantum tunneling in small systems

It is well known that quantum computers are superior to classical computers in efficiently simulating quantum systems. Here we report the first experimental simulation of quantum tunneling through potential barriers, a widespread phenomenon of a unique quantum nature, via NMR techniques. Our experiment is based on a digital particle simulation algorithm and requires very few spin-1/2 nuclei without the need of ancillary qubits. The occurrence of quantum tunneling through a barrier, together with the oscillation of the state in potential wells, are clearly observed through the experimental results. This experiment has clearly demonstrated the possibility to observe and study profound physical phenomena within even the reach of small quantum computers.Comment: 17 pages and 8 figure

Molecular Dynamics for Fermions

The time-dependent variational principle for many-body trial states is used to discuss the relation between the approaches of different molecular dynamics models to describe indistinguishable fermions. Early attempts to include effects of the Pauli principle by means of nonlocal potentials as well as more recent models which work with antisymmetrized many-body states are reviewed under these premises. Keywords: Many-body theory; Fermion system; Molecular dynamics; Wave-packet dynamics; Time-dependent variational principle; Statistical properties; Canonical ensemble; Ergodicity; Time averagingComment: 97 pages, 13 postscript figures. To be published in July 2000 issue of Reviews of Modern Physics. More information at http://www-aix.gsi.de/~fmd

Correlation dynamics of three spin under a classical dephasing environment

By starting from the stochastic Hamiltonian of the three correlated spins and modeling their frequency fluctuations as caused by dephasing noisy environments described by Ornstein-Uhlenbeck processes, we study the dynamics of quantum correlations, including entanglement and quantum discord. We prepared initially our open system with Greenberger-Horne-Zeilinger or W state and present the exact solutions for evolution dynamics of entanglement and quantum discord between three spins under both Markovian and non-Markovian regime of this classical noise. By comparison the dynamics of entanglement with that of quantum discord we find that entanglement can be more robust than quantum discord against this noise. It is shown that by considering non-Markovian extensions the survival time of correlations prolong.Comment: 13 pages, 4 figure