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We present an analytical study of the standard two-party deterministic dense-coding protocol, under which communication of perfectly distinguishable messages takes place via a qudit from a pair of non-maximally entangled qudits in pure state |S>. Our results include the following: (i) We prove that it is possible for a state |S> with lower entanglement entropy to support the sending of a greater number of perfectly distinguishable messages than one with higher entanglement entropy, confirming a result suggested via numerical analysis in Mozes et al. [Phys. Rev. A 71 012311 (2005)]. (ii) By explicit construction of families of local unitary operators, we verify, for dimensions d = 3 and d=4, a conjecture of Mozes et al. about the minimum entanglement entropy that supports the sending of d + j messages, j = 2, ..., d-1; moreover, we show that the j=2 and j= d-1 cases of the conjecture are valid in all dimensions. (iii) Given that |S> allows the sending of K messages and has the square roof of c as its largest Schmidt coefficient, we show that the inequality c <= d/K, established by Wu et al. [ Phys. Rev. A 73, 042311 (2006)], must actually take the form c < d/K if K = d+1, while our constructions of local unitaries show that equality can be realized if K = d+2 or K = 2d-1.Comment: 19 pages, 2 figures. Published versio

For one qubit systems, we present a short, elementary argument characterizing unital quantum operators in terms of their action on Bloch vectors. We then show how our approach generalizes to multi-qubit systems, obtaining inequalities that govern when a "diagonal" superoperator on the Bloch region is a quantum operator. These inequalities are the n-qubit analogue of the AlgoetFujiwara conditions. Our work is facilitated by an analysis of operator-sum decompositions in which negative summands are allowed.

The quantum behavior of a wave packet in a one-dimensional infinite square well with a finite barrier in the center is considered. Computer generated plots are presented that lead to useful analytic approximations for finding eigenvalues of the Schrödinger equation and for explaining the time dependence of wave packets.

A C-Language program which tabulates the isoscalar factors and Clebsch-Gordan coefficients for products of representations in SU (3) is presented. These are efficiently computed using recursion relations, and the results are presented in exact precision as square roots of rational numbers. Output is in L a T E X format.