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

Dynamical mapping method in nonrelativistic models of quantum field theory

The solutions of Heisenberg equations and two-particles eigenvalue problems for nonrelativistic models of current-current fermion interaction and $N, \Theta$ model are obtained in the frameworks of dynamical mapping method. The equivalence of different types of dynamical mapping is shown. The connection between renormalization procedure and theory of selfadjoint extensions is elucidated.Comment: 14 page

The Free Quon Gas Suffers Gibbs' Paradox

We consider the Statistical Mechanics of systems of particles satisfying the $q$-commutation relations recently proposed by Greenberg and others. We show that although the commutation relations approach Bose (resp.\ Fermi) relations for $q\to1$ (resp.\ $q\to-1$), the partition functions of free gases are independent of $q$ in the range $-1<q<1$. The partition functions exhibit Gibbs' Paradox in the same way as a classical gas without a correction factor $1/N!$ for the statistical weight of the $N$-particle phase space, i.e.\ the Statistical Mechanics does not describe a material for which entropy, free energy, and particle number are extensive thermodynamical quantities.Comment: number-of-pages, LaTeX with REVTE

Clear band formation simulated by dislocation dynamics

Dislocation Dynamics simulations of dislocations gliding across a random populations of Frank loops are presented. Specific local rules are developed to reproduce elementary interaction mechanisms obtained in Molecular Dynamics simulations. It is shown that absorption of Frank loops as helical turns on screw dislocations governs the process of clear band formation, because: (1) it transforms the loops into jogs on dislocations, (2) when the dislocations unpin, the jogs are transported along the dislocation lines, leading to a progressive clearing of the band and (3) the dislocations are re-emitted in a glide plane different from the initial one, allowing for a broadening of the band. It is also shown that a pile-up of dislocations is needed to form a clear band of finite thickness.У термінах дислокаційної динаміки представлено моделювання дислокацій, що перетинають розташовану випадковим чином сукупність петель Франка. Розроблені локальні правила для відтворення елементарних механізмів взаємодії, що отримані при моделюванні методом молекулярної динаміки. Показано, що поглинання петель Франка у вигляді гелікоїдальних витків на гвинтових дислокаціях визначає процес утворення вільних зон, оскільки: 1) воно перетворює петлі у східці на дислокаціях, 2) у випадку відкріплення дислокації східці переносяться вздовж ліній дислокацій і 3) дислокації знову надходять у площину ковзання, яка відрізняється від вихідної, забезпечуючи тим самим розширення вільної зони. Крім того, показано, що скупчення дислокацій необхідне для утворення вільної зони з кінцевою товщиною.В терминах дислокационной динамики представлено моделирование дислокаций, пересекающих расположенную случайным образом совокупность петель Франка. Разработаны локальные правила для воспроизведения элементарных механизмов взаимодействия, полученных при моделировании методом молекулярной динамики. Показано, что поглощение петель Франка в виде геликоидальных витков на винтовых дислокациях определяет процесс образования свободных зон, поскольку: 1) оно преобразует петли в ступеньки на дислокациях, 2) в случае открепления дислокации ступеньки переносятся вдоль линий дислокаций и 3) дислокации вновь поступают в плоскость скольжения, отличающуюся от исходной, обеспечивая тем самым расширение свободной зоны. Кроме того, показано, что скопление дислокаций необходимо для образования свободной зоны с конечной толщиной

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

Some Properties of the Computable Cross Norm Criterion for Separability

The computable cross norm (CCN) criterion is a new powerful analytical and computable separability criterion for bipartite quantum states, that is also known to systematically detect bound entanglement. In certain aspects this criterion complements the well-known Peres positive partial transpose (PPT) criterion. In the present paper we study important analytical properties of the CCN criterion. We show that in contrast to the PPT criterion it is not sufficient in dimension 2 x 2. In higher dimensions we prove theorems connecting the fidelity of a quantum state with the CCN criterion. We also analyze the behaviour of the CCN criterion under local operations and identify the operations that leave it invariant. It turns out that the CCN criterion is in general not invariant under local operations.Comment: 7 pages; accepted by Physical Review A; error in Appendix B correcte

Probabilistic implementation of universal quantum processors

We present a probabilistic quantum processor for qudits. The processor itself is represented by a fixed array of gates. The input of the processor consists of two registers. In the program register the set of instructions (program) is encoded. This program is applied to the data register. The processor can perform any operation on a single qudit of the dimension N with a certain probability. If the operation is unitary, the probability is in general 1/N^2, but for more restricted sets of operators the probability can be higher. In fact, this probability can be independent of the dimension of the qudit Hilbert space of the qudit under some conditions.Comment: 7 revtex pages, 1 eps figur

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

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

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 $s\leq (1+p^{n-1}) ^{-1}$