Exact and Asymptotic Measures of Multipartite Pure State Entanglement

In an effort to simplify the classification of pure entangled states of multi (m) -partite quantum systems, we study exactly and asymptotically (in n) reversible transformations among n'th tensor powers of such states (ie n copies of the state shared among the same m parties) under local quantum operations and classical communication (LOCC). With regard to exact transformations, we show that two states whose 1-party entropies agree are either locally-unitarily (LU) equivalent or else LOCC-incomparable. In particular we show that two tripartite Greenberger-Horne-Zeilinger (GHZ) states are LOCC-incomparable to three bipartite Einstein-Podolsky-Rosen (EPR) states symmetrically shared among the three parties. Asymptotic transformations result in a simpler classification than exact transformations. We show that m-partite pure states having an m-way Schmidt decomposition are simply parameterizable, with the partial entropy across any nontrivial partition representing the number of standard ``Cat'' states (|0^m>+|1^m>) asymptotically interconvertible to the state in question. For general m-partite states, partial entropies across different partitions need not be equal, and since partial entropies are conserved by asymptotically reversible LOCC operations, a multicomponent entanglement measure is needed, with each scalar component representing a different kind of entanglement, not asymptotically interconvertible to the other kinds. In particular the m=4 Cat state is not isentropic to, and therefore not asymptotically interconvertible to, any combination of bipartite and tripartite states shared among the four parties. Thus, although the m=4 cat state can be prepared from bipartite EPR states, the preparation process is necessarily irreversible, and remains so even asymptotically.Comment: 13 pages including 3 PostScript figures. v3 has updated references and discussion, to appear Phys. Rev.

Order reductions of Lorentz-Dirac-like equations

We discuss the phenomenon of preacceleration in the light of a method of successive approximations used to construct the physical order reduction of a large class of singular equations. A simple but illustrative physical example is analyzed to get more insight into the convergence properties of the method.Comment: 6 pages, LaTeX, IOP macros, no figure

Regulator constants and the parity conjecture

The p-parity conjecture for twists of elliptic curves relates multiplicities of Artin representations in p-infinity Selmer groups to root numbers. In this paper we prove this conjecture for a class of such twists. For example, if E/Q is semistable at 2 and 3, K/Q is abelian and K^\infty is its maximal pro-p extension, then the p-parity conjecture holds for twists of E by all orthogonal Artin representations of Gal(K^\infty/Q). We also give analogous results when K/Q is non-abelian, the base field is not Q and E is replaced by an abelian variety. The heart of the paper is a study of relations between permutation representations of finite groups, their "regulator constants", and compatibility between local root numbers and local Tamagawa numbers of abelian varieties in such relations.Comment: 50 pages; minor corrections; final version, to appear in Invent. Mat

Causality and Electromagnetic Transmissions Through Materials

There have been several experiments which hint at evidence for superluminal transport of electromagnetic energy through a material slab. On the theoretical side, it has appeared evident that acausal signals are indeed possible in quantum electrodynamics. However, it is unlikely that superluminal signals can be understood on the basis of a purely classical electrodynamic signals passing through a material. The classical and quantum theories represent quite different views, and it is the quantum view which may lead to violations of Einstein causality.Comment: Plain TeX, No figures, 5 page

Singularity-Free Electrodynamics for Point Charges and Dipoles: Classical Model for Electron Self-Energy and Spin

It is shown how point charges and point dipoles with finite self-energies can be accomodated into classical electrodynamics. The key idea is the introduction of constitutive relations for the electromagnetic vacuum, which actually mirrors the physical reality of vacuum polarization. Our results reduce to conventional electrodynamics for scales large compared to the classical electron radius $r_0\approx 2.8\times10^{-13}$ cm. A classical simulation for a structureless electron is proposed, with the appropriate values of mass, spin and magnetic moment.Comment: 3 page

Thermodynamics and the Measure of Entanglement

We point out formal correspondences between thermodynamics and entanglement. By applying them to previous work, we show that entropy of entanglement is the unique measure of entanglement for pure states.Comment: 8 pages, RevTeX; edited for clarity, additional references, to appear as a Rapid Communication in Phys. Rev.

Fields of accelerated sources: Born in de Sitter

This paper deals thoroughly with the scalar and electromagnetic fields of uniformly accelerated charges in de Sitter spacetime. It gives details and makes various extensions of our Physical Review Letter from 2002. The basic properties of the classical Born solutions representing two uniformly accelerated charges in flat spacetime are first summarized. The worldlines of uniformly accelerated particles in de Sitter universe are defined and described in a number of coordinate frames, some of them being of cosmological significance, the other are tied naturally to the particles. The scalar and electromagnetic fields due to the accelerated charges are constructed by using conformal relations between Minkowski and de Sitter space. The properties of the generalized `cosmological' Born solutions are analyzed and elucidated in various coordinate systems. In particular, a limiting procedure is demonstrated which brings the cosmological Born fields in de Sitter space back to the classical Born solutions in Minkowski space. In an extensive Appendix, which can be used independently of the main text, nine families of coordinate systems in de Sitter spacetime are described analytically and illustrated graphically in a number of conformal diagrams.Comment: 37 pages, 23 figures, reformatted version of the paper published in JMP; low-resolution figures due to arXiv size restrictions; for the version with high-resolution figures see http://utf.mff.cuni.cz/~krtous/papers

The Limits of Special Relativity

The Special Theory of Relativity and the Theory of the Electron have had an interesting history together. Originally the electron was studied in a non relativistic context and this opened up the interesting possibility that lead to the conclusion that the mass of the electron could be thought of entirely in electromagnetic terms without introducing inertial considerations. However the application of Special Relativity lead to several problems, both for an extended electron and the point electron. These inconsistencies have, contrary to popular belief not been resolved satisfactorily today, even within the context of Quantum Theory. Nevertheless these and subsequent studies bring out the interesting result that Special Relativity breaks down within the Compton scale or when the Compton scale is not neglected. This again runs contrary to an uncritical notion that Special Relativity is valid for point particles.Comment: 13 pages,Te

Exotic solutions in string theory

Solutions of classical string theory, correspondent to the world sheets, mapped in Minkowsky space with a fold, are considered. Typical processes for them are creation of strings from vacuum, their recombination and annihilation. These solutions violate positiveness of square of mass and Regge condition. In quantum string theory these solutions correspond to physical states |DDF>+|sp> with non-zero spurious component.Comment: accepted in Il Nuovo Cimento A for publication in 199

Helmholtz theorem and the v-gauge in the problem of superluminal and instantaneous signals in classical electrodynamics

In this work we substantiate the applying of the Helmholtz vector decomposition theorem (H-theorem) to vector fields in classical electrodynamics. Using the H-theorem, within the framework of the two-parameter Lorentz-like gauge (so called v-gauge), we show that two kinds of magnetic vector potentials exist: one of them (solenoidal) can act exclusively with the velocity of light c and the other one (irrotational) with an arbitrary finite velocity $v$ (including a velocity more than c . We show also that the irrotational component of the electric field has a physical meaning and can propagate exclusively instantaneously.Comment: This variant has been accepted for publication in Found. Phys. Letter