Quantum Surveying: How Entangled Pairs Act as Measuring Rods on Manifolds of Generalized Coherent States

Generalized coherent states arise from reference states by the action of locally compact transformation groups and thereby form manifolds on which there is an invariant measure. It is shown that this implies the existence of canonically associated Bell states that serve as measuring rods by relating the metric geometry of the manifold to the observed EPR correlations. It is further shown that these correlations can be accounted for by a hidden variable theory which is non-local but invariant under the stability group of the reference state.Comment: 14 pages, 0 figures, plain te

q- Deformed Boson Expansions

A deformed boson mapping of the Marumori type is derived for an underlying $su(2)$ algebra. As an example, we bosonize a pairing hamiltonian in a two level space, for which an exact treatment is possible. Comparisons are then made between the exact result, our q- deformed boson expansion and the usual non - deformed expansion.Comment: 8 pages plus 2 figures (available upon request

Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems

If quantum states exhibit small nonlinearities during time evolution, then quantum computers can be used to solve NP-complete problems in polynomial time. We provide algorithms that solve NP-complete and #P oracle problems by exploiting nonlinear quantum logic gates. It is argued that virtually any deterministic nonlinear quantum theory will include such gates, and the method is explicitly demonstrated using the Weinberg model of nonlinear quantum mechanics.Comment: 10 pages, no figures, submitted to Phys. Rev. Let

Separability and Fourier representations of density matrices

Using the finite Fourier transform, we introduce a generalization of Pauli-spin matrices for $d$-dimensional spaces, and the resulting set of unitary matrices $S(d)$ is a basis for $d\times d$ matrices. If $N=d_{1}\times d_{2}\times...\times d_{b}$ and H^{[ N]}=\bigotimes H^{% [ d_{k}]}, we give a sufficient condition for separability of a density matrix $\rho$ relative to the $H^{[ d_{k}]}$ in terms of the $L_{1}$ norm of the spin coefficients of $\rho >.$ Since the spin representation depends on the form of the tensor product, the theory applies to both full and partial separability on a given space $H^{[ N]}$% . It follows from this result that for a prescribed form of separability, there is always a neighborhood of the normalized identity in which every density matrix is separable. We also show that for every prime $p$ and $n>1$ the generalized Werner density matrix $W^{[ p^{n}]}(s)$ is fully separable if and only if $s\leq (1+p^{n-1}) ^{-1}$

Search for exchange-antisymmetric two-photon states

Atomic two-photon J=0 $\leftrightarrow$J'=1 transitions are forbidden for photons of the same energy. This selection rule is related to the fact that photons obey Bose-Einstein statistics. We have searched for small violations of this selection rule by studying transitions in atomic Ba. We set a limit on the probability $v$ that photons are in exchange-antisymmetric states: $v<1.2\cdot10^{-7}$.Comment: 5 pages, 4 figures, ReVTeX and .eps. Submitted to Phys. Rev. Lett. Revised version 9/25/9

Passage of Time in a Planck Scale Rooted Local Inertial Structure

It is argued that the `problem of time' in quantum gravity necessitates a refinement of the local inertial structure of the world, demanding a replacement of the usual Minkowski line element by a 4+2n dimensional pseudo-Euclidean line element, with the extra 2n being the number of internal phase space dimensions of the observed system. In the refined structure, the inverse of the Planck time takes over the role of observer-independent conversion factor usually played by the speed of light, which now emerges as an invariant but derivative quantity. In the relativistic theory based on the refined structure, energies and momenta turn out to be invariantly bounded from above, and lengths and durations similarly bounded from below, by their respective Planck scale values. Along the external timelike world-lines, the theory naturally captures the `flow of time' as a genuinely structural attribute of the world. The theory also predicts expected deviations--suppressed quadratically by the Planck energy--from the dispersion relations for free fields in the vacuum. The deviations from the special relativistic Doppler shifts predicted by the theory are also suppressed quadratically by the Planck energy. Nonetheless, in order to estimate the precision required to distinguish the theory from special relativity, an experiment with a binary pulsar emitting TeV range gamma-rays is considered in the context of the predicted deviations from the second-order shifts.Comment: 17 pages; Diagram depicting "the objective flow of time" is replaced with a much-improved diagra

Asymmetric universal entangling machine

We give a definition of asymmetric universal entangling machine which entangles a system in an unknown state to a specially prepared ancilla. The machine produces a fixed state-independent amount of entanglement in exchange to a fixed degradation of the system state fidelity. We describe explicitly such a machine for any quantum system having $d$ levels and prove its optimality. We show that a $d^2$-dimensional ancilla is sufficient for reaching optimality. The introduced machine is a generalization to a number of widely investigated universal quantum devices such as the symmetric and asymmetric quantum cloners, the symmetric quantum entangler, the quantum information distributor and the universal-NOT gate.Comment: 28 pages, 3 figure

Contribution to understanding the mathematical structure of quantum mechanics

Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule, commutation and uncertainty relations, probability density current, momentum operator, rules for including the scalar and vector potentials and antiparticles can be obtained from the probabilistic description of results of measurement of the space coordinates and time. Equations of motion of quantum mechanics, the Klein-Gordon equation, Schrodinger equation and Dirac equation are obtained from the requirement of the relativistic invariance of the space-time Fisher information. The limit case of the delta-like probability densities leads to the Hamilton-Jacobi equation of classical mechanics. Many particle systems and the postulates of quantum mechanics are also discussed.Comment: 21 page

Anyonic behavior of quantum group gases

We first introduce and discuss the formalism of $SU_q(N)$-bosons and fermions and consider the simplest Hamiltonian involving these operators. We then calculate the grand partition function for these models and study the high temperature (low density) case of the corresponding gases for $N=2$. We show that quantum group gases exhibit anyonic behavior in $D=2$ and $D=3$ spatial dimensions. In particular, for a $SU_q(2)$ boson gas at $D=2$ the parameter $q$ interpolates within a wider range of attractive and repulsive systems than the anyon statistical parameter.Comment: LaTeX file, 19 pages, two figures ,uses epsf.st

Quantum information distributors: Quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit

We show that for any Hilbert-space dimension, the optimal universal quantum cloner can be constructed from essentially the same quantum circuit, i.e., we find a universal design for universal cloners. In the case of infinite dimensions (which includes continuous variable quantum systems) the universal cloner reduces to an essentially classical device. More generally, we construct a universal quantum circuit for distributing qudits in any dimension which acts covariantly under generalized displacements and momentum kicks. The behavior of this covariant distributor is controlled by its initial state. We show that suitable choices for this initial state yield both universal cloners and optimized cloners for limited alphabets of states whose states are related by generalized phase-space displacements.Comment: 10 revtex pages, no figure