We show that the Lawrence–Krammer representation is unitary. We explicitly present the non-singular matrix representing the sesquilinear pairing invariant under the action. We show that reversing the orientation of a braid is equivalent to the transposition of its Lawrence–Krammer matrix followed by a certain conjugation. As corollaries it is shown that the characteristic polynomial of the Lawr...

In this paper we discuss an approach to quantum computation where the basic information units (qubits and quregisters) are replaced by density operators and the restriction to unitary operators as logical gates is lifted through the introduction of the more general concept of quantum operation ( [17], [1]). This perspective is especially suited to provide a physical description of open systems....

Effects of strychnine on intraretinal inhibition were investigated by recording unitary discharges from the optic tract fibers. Units were classed as on, off and on off according to their discharge patterns in response to diffuse illumination of the retina. Strychnine enhanced the firing rate of spontaneous discharge in the dark. ' On' inhibition of an off unit was greatly suppressed by strychn...

We investigate the following two problems on a hermitian form Φ over an algebraic number field: (1) classification of Φ over the ring of algebraic integers; (2) hermitian Diophantine equations. The same types of problems for quadratic forms were treated in the author’s previous articles. Here we discuss the hermitian case. Problem (2) concerns an equation ξΦ · ξ = Ψ , where Φ and Ψ represent he...

Network sampling and classical survey sampling differ with respect to the counting rule paradigm for linking population elements to the selection units at which they are countable in the survey [20]. Classical survey sampling uses unitary counting rules, such as de jure and de facto residence rules in household surveys, that seek to uniquely link each person to one and only household. Network s...

In multimode fiber transmission systems, mode-dependent loss and gain (collectively referred to as MDL) pose fundamental performance limitations. In the regime of strong mode coupling, the statistics of MDL (expressed in decibels or log power gain units) can be described by the eigenvalue distribution of zero-trace Gaussian unitary ensemble in the small-MDL region that is expected to be of inte...