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We present an extended version of max-plus algebra which includes the inverse operator of “max.” This algebra enables us to ultradiscretize the system including subtractions and obtain new ultradiscrete equations. The known ultradiscrete equations can also be recovered by this construction. [ABSTRACT FROM AUTHOR]

A basis of N2 projectors, each an N2×N2 matrix with constant elements, is implemented to construct a class of braid matrices R⁁(θ), θ being the spectral parameter. Only odd values of N are considered here. Our ansatz for the projectors Pα appearing in the spectral decomposition of R⁁(θ) leads to exponentials exp(mαθ) as the coefficient of Pα. The sums and differences of such exponentials on the diagonal and the antidiagonal, respectively, provide the (2N2-1) nonzero elements of R⁁(θ). One element at the center is normalized to unity. A class of supplementary constraints imposed by the braid equation leaves 1/2(N+3)(N-1) free parameters mα. The diagonalizer of R⁁(θ) is presented for all N. Transfer matrices t(θ) and L(θ) operators corresponding to our R⁁(θ) are studied. Our diagonalizer signals specific combinations of the components of the operators that lead to a quadratic algebra of N2 constant N×N matrices. The θ dependence factors out for such combinations. R⁁(θ) is developed in a power series in θ. The basic difference arising for even dimensions is made explicit. Some special features of our R⁁(θ) are discussed in a concluding section. [ABSTRACT FROM AUTHOR]

The Hughston–Jozsa–Wootters theorem shows that any finite ensemble of quantum states can be prepared “at a distance,” and it has been used to demonstrate the insecurity of all bit commitment protocols based on finite quantum systems without superselection rules. In this paper, we prove a generalized HJW theorem for arbitrary ensembles of states on a C*-algebra. We then use this result to demonstrate the insecurity of bit commitment protocols based on infinite quantum systems, and quantum systems with Abelian superselection rules. [ABSTRACT FROM AUTHOR]

If a state is passive for uniformly accelerated observers in n-dimensional (n>=2) anti–de Sitter (Ads) space–time (i.e., cannot be used by them to operate a perpetuum mobile), they will (a) register a universal value of the Unruh temperature, (b) discover a PCT symmetry, and (c) find that observables in complementary wedge-shaped regions necessarily commute with each other in this state. The stability properties of such a passive state induce a “geodesic causal structure” on AdS and concommitant locality relations. It is shown that observables in these complementary wedge-shaped regions fulfill strong additional independence conditions. In two-dimensional AdS these even suffice to enable the derivation of a nontrivial, local, covariant net indexed by bounded space–time regions. All these results are model-independent and hold in any theory which is compatible with a weak notion of space–time localization. Examples are provided of models satisfying the hypotheses of these theorems. [ABSTRACT FROM AUTHOR]